Unit 3 (Part 1 of 2): Lines (Lessons 3-1 through 3-7) · Special Types of Linear Graphs Horizontal Lines Horizontal lines only travel through the y-axis, no x-intercept here! Equation:

Name: ______________________________

Geometry Period _______

Unit 3 (Part 1 of 2): Lines

(Lessons 3-1 through 3-7) In this unit you must bring the following materials with you to class every day:

Calculator

Pencil

This Booklet

A device

Headphones

Please note:

You may have random material checks in class

Some days you will have additional handouts to support your understanding of

the learning goals in that lesson. Keep these in a folder and bring to class

everyday.

All homework for part one of this unit is in this booklet.

Answer keys will be posted as usual for each daily lesson.

Today’ Learning Goal: How do you graph and write linear equations?

Do Now-Reactivate your knowledge!

What do you know about linear equations? Write anything that comes to mind. What do they look like?

Together: Let’s describe the lines shown below: use the word bank to help you!

Now, look at the equations. How do your observations fit into the equation?

Slope-Intercept Form of a Linear Equation

How can you recognize the slope? What does the slope represent?

How can you recognize the y-intercept? What does the y - intercept represent?

Looking ahead: This is NOT the only form of a line, next class we will talk about the point slope form of a line.

Algebra Review: Rewrite the following equation in y= mx+b form: 𝑦 + 7 = 1

7𝑥 − 1

3-1 Notes

Word Bank Increasing Decreasing Fast rate of change Slower rate of change Positive slope Negative slope

----Group Practice----

Look for your job’s symbol now, so you know when it takes place!

STATION 1: DETERMINING SLOPE AND Y-INTERCEPT GIVEN AN EQUATION

In the next few examples we will have to determine the slope and y-intercepts of the equations given to us.

Let’s be careful though, because for these equations, we will have to re-write them in y = mx + b form first!

As a team! Determine the slope and y-intercept of the equations below:

a) −3𝑥 – 2𝑦 = −2 b) 5𝑥 – 2𝑦 = −2

Now work backwards:

c) Write the equation of a line whose slope is −2

3 and whose 𝑦 intercept is 3

Special Types of Linear Graphs

Horizontal Lines Horizontal lines only travel through the y-axis, no x-intercept here! Equation: y = -1 Slope = 0

Vertical Lines Here, because the line doesn’t travel through the y-axis, we need an x-intercept. Equation: x = -2 Slope: undefined

Slope: ___________ y-int: ___________ Slope: ___________ y-int: ___________

STATION #2: WRITING THE EQUATION OF A LINE GIVEN A GRAPH IN SLOPE-INTERCEPT FORM

As a team! Write the equations of the line graphed below!

Steps as we Go! Guided Example: Determine the equation for the following graphed line

Before we start, we know for any linear equation, we need a slope, and a y-intercept! We will solve for slope 1st

Part I. Determining the slope

1. Pick 2 clean points 2. Select the left most point. Count how many units

vertically it takes so it’s on the same level as the 2nd point. Then count how many units horizontally it takes to get to the 2nd point

3. Plug in: 𝑚 =𝑟𝑖𝑠𝑒

𝑟𝑢𝑛=

𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑦

𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑥

Part II. Writing the equation: 1. Make sure you have the slope (m) 2. Find the y-intercept (where does the line cross the y-

axis?) (b) 3. Plug into y = mx + b!

STATION #3: GRAPHING LINEAR EQUATIONS

Steps as you go! Guided example: Graph 𝑦 − 3 = −2𝑥

1. Get into y = mx+ b form!

2. Identify your slope and y-intercept

3. Begin with b –plot the y-intercept

4. Move with respect to slope

5. Plot at least points using slope pattern until the end of page.

6. Construct with arrows and label

Now you Try!

Graph: 𝑦 − 4 = 3

2𝑥 − 1

STATION #4: RECOGNIZING LINEAR EQUATIONS AND LINEAR RELATIONSHIPS

If an equation is a linear equation, the variable 𝒙

Exception! If variable X has a power of one but the variable y has a power of zero, it will be a linear relation, but not a

function of x. Example 𝑥1 = 𝑦0 + 7 simplifies to 𝑥 = 7.

As a team! Are the following linear equations? If they are, re-write in y=mx+b form if possible. If NOT, explain how you know.

1. 𝑦 = 2𝑥 − 3

2. .

3. 4𝑥 + 5𝑦 = 20

4. y = 3x2 + 12x + 1

NOTATION:

If the diagram of equation is a line the symbol is ⟷ and we will see ARROWS in both ends.

o Example: 𝐴𝐵 ⃡ (this is a line that travels through a point A and a point B)

If the diagram of equation is a line the symbol is − and we will see ENDPOINTS in both ends.

o Example:𝐴𝐵̅̅ ̅̅ (this is a line segment that starts at point A and ends at point B)

Has a power power of zero ( which converts the x

into 1) AND the variable y has a power of 1.

Example: 𝑦 = 𝑥0 + 7 simplifies to 𝑦 = 8

Has a power power of one AND the variable y has a

power of 1. Example: 𝑦 = 𝑥1 + 7 simplifies to

𝑦 = 𝑥 + 7

Mixed Practice!

1) Based on the equations below state the slope (m) and y-intercept in simplest form.

a) 𝑦 + 2 = 𝑥 b) 5𝑦 + 10 = 15x c) 1

2𝑥 − 𝑦 = 4

2) State the x-intercept and y-intercept of the graph shown right:

x-intercept: ___________

y-intercept: ___________

3) Graph the line: y = -x+ 1 Hint: it may be helpful to state the y-intercept and slope before graphing

4) Circle the linear functions: 3𝑥 + 4𝑦 = 7 𝑦 = 𝑥2 + 2 𝑥 = 7

5) Represent “line CD” using appropriate notation:

Check Out!

Select one of the following columns to fill in. The right column is meant to challenge you.

1) Write the equation of a line with a slope of −3

4 and a y-

intercept of 3.

1) Write the equation of a line with a slope of 4 and containing the point (2,1)

2) Graph the line whose equation you found in #1


3) State the slope and y-intercept of the equation:

2𝑦 − 2 = 4𝑥

3) State the slope and y-intercept of the equation:

3-1 Homework Directions: For each number, choose a question either from the left or right column. Each column helps you practice

the same content, but the right column allows you to challenge yourself. FILL OUT LOOKING FORWARD!

1) Determine the slope and y-intercept of the following equations. 1) y = -2x - 1 2) a) 2y = 5x + 4 3) Explain how #1 and 2 above were different. What is the important step that you needed to take to find the slope and y-intercept? 4) Write the equation of a line whose slope is ½ and y-intercept is 0.

1) Determine the slope and y-intercept of the following equation.

4x – 3y = 5 2) Do the lines below have the same slope, same y-intercept, or neither? Justify your answer.

3y - 4x = 5 and 4y + 6 = 3x

3) Explain how you were able to determine if the lines from #2 had the same slope and y-intercept. 4) Write the equation of a line whose slope is ½ and passes through the origin.

5) a) Determine the coordinates of the y-intercept and the x-intercept of the graph below. b) Using the graph above: Determine: y-intercept: __________ slope: __________ Equation: ______________________

6) Graph the line −𝑦 =2

3𝑥 − 2

5) Graph a line that has the points (-4,-2) and (4,6). Determine the coordinates of the x-intercept and y-intercept. b) Determine the equation of the line graphed above.

6) Graph the line:𝑦 − 3 = −2

3(𝑥 + 1)

Today’ Learning Goal: How do you graph and write linear equations in point-slope form?

Reactivate your knowledge!

What do you know about linear equations?

What do they look like?

Warm-Up: Determine the equation for the following graphed line

New Vocab Alert!! POINT-SLOPE FORM of a Line

While we may be more comfortable with slope-intercept form,

there is another way to write the equation of the line called point-

slope form. Let’s take a look at it!

Using just a single point on the line and the slope you can fill in and write the equation! Check it out!

Guided Example Write the equation of a line that goes through the point (3,-2) with a slope of 4.

3-2 Notes

The end! No need to simplify further!

Let’s try it…

Using the graph of the line below, answer a-d below.

Let’s try it again…

Write equations of lines in point-slope form!

a) Write the equation of a line that goes through the point (2,7) with a slope of 3.

b) Write the equation of a line that goes through the point

(-1,4) with a slope of 1

3.

Graphing a Line, given point-slope form: Graph the line: y-1 = 2(x+ 1) Hint: it may be helpful to state a point on the line and slope before graphing!

a) Write the coordinates of a point that lies on the line.

b) What is the slope of the line?

c) Write the equation for the line in point-slope form.

d) Is this the same as our Warm-Up? How can we check?

Lesson Summary:

What is the general form of slope-intercept equation of a line: _____________________________

What is the general form of point-slope equation of a line: ________________________________

When graphing a line from point-slope, remember to ____________________ of the

x- and y-coordinates!

Change the following point-slope into slope-intercept: ONLY DO THIS IF THE QUESTION ASKS YOU TO!

𝑦 − 2 =1

2(𝑥 + 2) What’s the slope and y-intercept?

Mixed Practice! 4) State the equation of the line graphed to the right in point-slope form:

5) Graph the following linear equation on the graph below.

𝑦 − 6 = −3

2(𝑥 + 7)

Exit Ticket - Raise your hand when you are ready to check your answers

4) Write the equation of a line with a slope of 4 and containing the point (-2,1) in point-slope form.


6) State the slope and a point on the line from the equation:

y + 6 = -2(x-3)

3-2 Homework Directions: Answer each question below. Don’t forget to check in with the answer key when you are done!

1) Write the equation of a line whose slope is ½ and x-intercept is 0.

2) Determine the coordinates of any point on the line and the slope.

(x,y): __________

slope: __________

Equation in point-slope form: ______________________

3) Graph the line −𝑦 =2

3𝑥 − 2

4) Do the lines below have the same slope or y-intercept? Justify your answer.

2y - 4x = -3 and 4y + 6 = 3x

5) Write the equation of a line whose slope is ½ and passes through the point (-4,1).

6) a) Graph a line that has the points (-4,-2) and (4,4).

b) Determine the coordinates of the y-intercept.

c) Determine the equation of the line graphed above.

7) Graph the line:𝑦 − 3 = −2

3(𝑥 + 1)

Lesson 3-3: Linear Relationships

Learning Goal: Can I determine whether lines are parallel, perpendicular, neither, or the same line given the equation of the lines? Can I justify my responses to these questions?

Let’s Start Together Complete the following chart using what you know about the following types of lines.

Let’s Discover on the Coordinate Plane – What is the special relationship between parallel lines and perpendicular lines?

1) Use the graph shown right to answer each of the following questions:

Partner 1 Partner 2

Line 1 Line 2

a) State a point on line 1


b) State the slope of line 1

b) State the slope of line 2( simplify Fraction)

c) Use point-slope form to write the equation of line 1


Share answers from above with your partner, then answer d-f: d) Are the y-intercepts the same? e) Is anything the same about these two lines? f) Are the lines parallel, perpendicular or neither?

3-3 Notes

Next

Symbol

Symbol

2) Use the graph shown right to answer each of the following questions:

Partner 1 Partner 2

Line 1 Line 2



b) State the slope of line 1

b) State the slope of line 2 (as a fraction over 1)



Share answers from above with your partner, then answer d-f: d) Is anything the same about these two lines? e) How do the slopes relate to each other? f) Are the lines parallel, perpendicular or neither?

Eureka! We discovered the relationship! Let’s share our findings with our classmates!

Linear Relationships

Parallel lines have _________________________________________________________.

Perpendicular lines have _____________________________________________________.

Game Plan:

Let’s try it together!

1. Determine whether the following lines are parallel, perpendicular, neither, or the same line? Justify your equation in words.

7 + 𝑦 = 4𝑥 −3 = −1

4𝑥 − 𝑦

My Thinking Space:

1. Given the equation of the line, ____________________________ Write the equation of a line parallel to it and that travels through the point (3,5) Use point slope! Copy answer on whiteboard once you compared with your elbow partner! 2. Are the following lines parallel, perpendicular, neither, or the same line? Justify your answer using mathematics.

Copy answer on whiteboard once you compared with your elbow partner!

Copy from board

3. Are the following lines parallel, perpendicular, neither, or the same line? Prove your answer.

Copy answer on whiteboard once you compared with your elbow partner! 4. Are the following lines parallel, perpendicular, neither, or the same line? Prove your answer.

Copy answer on whiteboard once you compared with your elbow partner!

Answer the first two problems (3-1 and 3-2) in your looking forward!

3-3 HOMEWORK

Watch the assigned video and try the example on this page. Mastery of the content of

this video is essential for our next lesson in class. Failure to watch the video will result

in confusion and your inability to interact with your peers throughout the lesson. This

page will be checked tomorrow in class and an entrance ticket into class will be

assigned to prove your mastery of the concept.

Get on your EdPuzzle!!! I’m looking for you…

a) In this video, we are learning how to ________________________________________________________________.

b) In the space provided, copy down the notes and follow along with the example being presented in this video. You

will have a chance to further practice this skill!

c) You try! Write the equation of a line (in point-slope form) that is parallel to the line y = -2x + 5 and goes through

the point (3,4).

Keep going, don’t forget to check key!

Directions: For each number, choose a question either from the left or right column. Each column helps you practice

the same content, but the right column allows you to challenge yourself.

1) 1) What is the slope of a line perpendicular to the line whose equation is ?

2) Write equations of three lines that are parallel to the line with equation y =3.5x -2. 3) Determine whether the graph of -4y = -x+5 and -16x- 4y = 9 are perpendicular lines. 4) Which equation represents a line that is perpendicular

to the line represented by ?

1)

2)

3)

4)

1) What is the slope of a line perpendicular to the line whose equation is ?

2) Determine whether AB CD or AB CD.

A(1,5), B(3,9), C(2,2), D(4,6) 3) Determine the value x so that a line containing

(6, 2) and (x, -1) has a slope of −3

7. Then graph the line.

4) Which equation represents a line that is perpendicular to

the line represented by ?

1)

2)

3)

4)

Writing Equations

Learning Goals: How can I use prior understanding of parallel lines to predict the process of writing equations of

perpendicular lines?

Summary!

3-4 Notes

A little bit of discovery

1. The slope of a line is m=2, what is the slope of a line perpendicular to it?

2. Last night you worked on finding equations of line parallel to a given line through a point.

Predict and discuss how the process would change if we wanted the new line to be

Perpendicular to the old line through a given point?

If I Know:

That our new

line is

PARALLEL to

the given line.

A point on the

new line.

If I Know:

That our new line

is PERPENDICULAR

to the given line.

A point on the new

line.

Done!

Done!

Do this

only if

asked!

Do this

only if

asked!

Let’s try some together!

1. What is the equation of a line that passes through the point (3,1) and is parallel to 2y-4x = 6 .

Think! Did the question indicate what type of equation to use in your answer?

2. What is the equation of a line perpendicular to y = 2x3

2 , and passes through the point (2,- 4) (Use slope-

intercept form)

Your Turn to Practice!

Directions: Work with your group members to answer the following questions. Show all work.

1. What is the equation of a line that passes through the point and is parallel to the line whose equation is

?

2. What is the equation of a line that passes through the point (-1,-2) and is perpendicular to -5x = 6y + 18?

3. Write the equation of a line that is parallel to 4x + 2y = -8 and has the same y-intercept as -3y = -2x – 9.

4. Find the equation of the line that is perpendicular to the line that passes through the points (–2, 4) and (1, 2) and

intersects that line at (1,2).

Rescue me!

We are going to play mad libs! Write the names of two random people in your group

𝑃𝐸𝑅𝑆𝑂𝑁 #1

𝑃𝐸𝑅𝑆𝑂𝑁 #2 .

Now add the names to the story before answering the

𝑃𝐸𝑅𝑆𝑂𝑁 #1 sees a baseball heading straight for her friend

𝑃𝐸𝑅𝑆𝑂𝑁 #2 .

𝑃𝐸𝑅𝑆𝑂𝑁 #2 has no idea that he/she is

about to be hit by a baseball. Sketch (with a straightedge) the path of the baseball to person #2.

𝑃𝐸𝑅𝑆𝑂𝑁 #1 decides to run and catch the baseball along its path.

𝑃𝐸𝑅𝑆𝑂𝑁 #1 is located at (-6,8) .

𝑃𝐸𝑅𝑆𝑂𝑁 #2 is

at (-6,-7). The baseball is currently at (7,7) and closing fast.

1. What is the equation of the line that shows the baseballs path? ( line that passes through

PERSON #2 and

the baseball.)

2. If

𝑃𝐸𝑅𝑆𝑂𝑁 #1 runs along the path of the shortest distance (which is the line perpendicular to the path of

the baseball), what is the equation in point-slope form of the line that follows that path? (Use steps from

today!)

Extension: Place and “star symbol” on point where she intercept the ball! Graph the lines with a ruler!

Extra Time Extension Problem

3-4 Homework

Directions: For each number, choose a question either from the left or right column. Each column helps you practice

the same content, but the right column allows you to challenge yourself.

1) Describe and write the equation of a line with zero slope and where the y-intercept is -3. 2) Using point-slope form, write the equation of a line parallel to 2y – 4x = 1, that passes through the point (-2, 1). Graph both lines below.

1) Describe and write the equation of a line with undefined slope and where the x-intercept is 2. 2) Using point-slope form, write the equation of a line parallel to 35y – 7x = -21, that passes through the point

(−5

3, 1). Graph both lines below.

Watch the assigned video and try the example on this page. Mastery of the content of

this video is essential for our next lesson in class. Failure to watch the video will result

in confusion and your inability to interact with your peers throughout the lesson. This

page will be checked tomorrow in class and an entrance ticket into class will be

assigned to prove your mastery of the concept.

Video is on Edpuzzle!

In this video, we are learning how to ________________________________________________________________.

In the space provided, copy down the notes and follow along with the example being presented in this video. You will

have a chance to further practice this skill!

Try it! Find the slope of the line segment joining the points ( 1, - 4) and ( - 4, 2 )

3) Using slope-intercept form, write the equation of a line perpendicular to

y = 2x3

2 , that also passes through the point (2,4)

3) Using slope-intercept form, write the equation of a line perpendicular to

y = 2x3

2 , that also passes through the point (-

7.5,2.5)

Slope

Learning Goal: How do you determine the slope and the equation of a line when given two points on that line?

*We need to find the slope when we have two points on the line (we don't have the equation of the line).

Point 1 (x1, y1) Point 2 (x2, y2)

Method 1

Graphically

Method 2

Slope Formula ( yes –we MUST know this formula)

Very Important: Slope is ALWAYS, change in y over change in x

Tips for Success: Slope

1) Simplify your fractions 2) Watch out for double negatives 3) Change in y over change in x

4) Negative fraction come in many forms 5) Label points x1, y1 and x2, y2

3-5 Notes

Let's Apply It!

Given quadrilateral ABCD, with points 𝐴(−7, 5), 𝐵(−4, 8), 𝐶(−1, 5) and 𝐷(−5, 0).

Find the slope of each side of the quadrilateral.

What can you infer about the sides AB and BC?

Self-Assess for success! Where do you rank yourself today???

Rank #:

3-5 Homework Directions: Answer all questions to the best of your ability showing all work!

1) Use the slope formula to find the slope of 𝐴𝐵̅̅ ̅̅ with 𝐴(−3,5) and 𝐵(8, −2).

2) Write the equation of a line that goes through 𝐶(10, −7) and 𝐷(20, −3).

What can you infer?

3) Quadrilateral JKLM has vertices as follows: 𝐽(−3,5), 𝐾(7,5), 𝐿(10, −2), and 𝑀(1, −2). Find the slope of all 4 sides

and state any inferences you can make.

Watch the assigned video and try the example on this page. Mastery of the content

of this video is essential for our next lesson in class. Failure to watch the video will

result in confusion and your inability to interact with your peers throughout the

lesson. This page will be checked tomorrow in class and an entrance ticket into class

will be assigned to prove your mastery of the concept.

Video in Edpuzzle!

d) In this video, we are learning how to ________________________________________________________________.

e) Midpoint Formula:

f) In the space provided, copy down the notes and follow along with the example being presented in this video. You

will have a chance to further practice this skill!

You try! Find the midpoint of the segment connecting the points (6,4) and (3,-4).

Length and Midpoint Learning Goals: How do we determine the length of a segment? How can we determine the midpoint of a segment?

Let's Get it Started!

1) Brainstorm- What is distance? (Think geometrically)

2) What word/s do you think of when you hear “MIDPOINT?”

3) Can we find the distance between points A and C? How?

4) Can we find the distance between points A and B? How?

Finding Length Midpoint

The distance formula tells us: Midpoint:

The Distance Formula

Can you think of a type of line

that goes through a midpoint?

The Midpoint Formula

3-6 Notes

Memorize these!

Finding Length (or distance): EXAMPLE 1:

a) Given Quadrilateral ABCD with vertices: A (-6, 3), B (6, 8), C(4,-1) and D(-8,-6). Find the length of each side. Together Your Turn D(AB) = D(CD) =

b) What do we know about sides AB and CD?

c) Find the midpoint of diagonal AC

Midpoint (AC) =

EXAMPLE 2: The midpoint of AB is M(4,2). If the coordinates of A are (6,-4), what are the coordinates of B?

3-6 Practice

3-6 Homework Directions: Answer the following questions to the best of your ability. Show all work to earn full credit. FILL OUT LOOKING FORWARD! 1) M is the midpoint of AB. The coordinates of A are (-2,3) and the coordinates of B are (3,1). Find the coordinates of M.

2) Find the distance between the points (-4,-5) and (1,-2).

3) If AB are the endpoints of a line with midpoint M, and A(3,0) and M(-2,8), find the other endpoint.

4) The points (5,4) and (1,0) are at opposite ends of the diameter of a circle.

a) What is the center of the circle, given that it is halfway between the two points given on the circle?

b) What is the length of the radius of this circle if the radius is the distance between the center and one of the points on the circle?

5) The endpoints of a line segment are A(a, -b) and B(3a+2, 3b -4). What is the midpoint of this segment in terms of a and b.

6) In the graph below, triangle PRQ was reflected over the line x-axis to map onto triangle P’R’Q’.

a) With a straightedge connect point Q and point Q’ to make line segment 𝑄𝑄′̅̅ ̅̅ ̅.

b) With a geometric compass, construct the perpendicular bisector of 𝑄𝑄′̅̅ ̅̅ ̅ on the graph provided.

c) What do you notice about the perpendicular bisector you just constructed, with respect to the rigid motion that occurred above?

Lesson 3-7: Perpendicular Bisector Equation

Learning Goal: How do we write the equation of a perpendicular bisector?

Conceptual Foundations Consider the following three diagrams:

Classification:

Classification:

Classification:

Reason:

Reason:

Reason:

Using the word bank, classify the type of line the blue line is. Use details from the diagram to justify your response!

Big Idea 1): If I want to write an equation of a perpendicular bisector through a line segment, what point MUST I use to plug into the equation? Big Idea 2): If I want to write an equation of a perpendicular bisector through a line segment, what MUST be true about the slope I use compared to the slope of the original line segment?

3-7 Notes

Word Bank: (one will not be used)! Perpendicular

Bisector Angle bisector

Perpendicular bisector

To write the equation of the perpendicular bisector of a segment: Now, let’s try together!

1) Write the equation of the perpendicular bisector of segment A(4,2) and B(8,6).

2) Justify that the line 𝑦 − 1 = −3

4(𝑥 − 2) is the perpendicular bisector of 𝐴𝐵̅̅ ̅̅ .

Note: Now we work backwards to confirm that the slopes are opposite reciprocals and this line contains the midpoint

a) If this line is the perpendicular bisector, then slopes should be

_______________________________. Are they? Check!

b) If this line is the perpendicular bisector, then the point should be ______________________. Is it? Check!

In conclusion:

Substitute both parts into

𝑦 − 𝑦1 = 𝑚(𝑥 − 𝑥1)

Substitute both parts into

Teacher will place a check

in each box for each

correct answer in warm

up:

PRACTICE!

Directions: Complete the following questions beginning with the “warm ups.” Once you have completed at least two of

the warm-ups, come check your answers and you may move onto the “jog.” After completing the jog and checking your

answers online, go for the “sprint!”

WARM-UP:

1) A line that passes through a point will bisect the segment that is formed by the points A (0, 5)

and B (8, 7). What are the coordinates of that point?

2) What is the length of segment XY if X (-2, 4) and Y (9, 12)?

3) Find the slope of the segment connecting the points (1,-3) and (2,8). What is the slope of a line perpendicular to this

segment?

Run the distance- don’t stop at the midpoint or take the shortcut along the perpendicular

bisector! Take these sprints all the way and exercise your brain!

JOG:

4) M is the midpoint of AB. The coordinates of A are (-2,3) and the coordinates of M are (1,0). Find the coordinates of B.

5) Write the equation of the line that bisects a segment with the endpoints (-6, 6) and (2, -2) and the line has a has a slope

of 1

2.

6) Line segment JK, has point J(-4, 5) and K(-2, 9). Find the equation of the perpendicular bisector

of JK.

7) In circle O, a diameter has endpoints (−5,4) and (3,−6). What is the length of the diameter?

SPRINT:

8) In circle G, diameter HI has endpoints H (2a, 3b -4) and I(2a-8, 5b+4). Find the coordinates of point G in terms of A and B

in simplest form.

9) Write the equation of the line that bisects a segment with the endpoints (-6, 6) and (2, -2) and is perpendicular to the

line 2y = x + 5.

10) The length of a line segment is √89. The endpoints are A(−1, y) and B(7,4)? Solve for all possible values of y

11) A triangle has vertices L(0, 6), M(6, 8), and N(4, −1). If point O is (5,3.5), is LO the altitude of the triangle.

Explain your reasoning.

3-7 HOMEWORK

1) Let’s summarize some of the main ideas in this unit so far!

a) To determine if lines or line segments are parallel, perpendicular or neither what would you look for? What formula would be necessary to use? Write the formula below.

b) To determine if line segments have the same length which formula would you use?

c) To determine if a given line is a perpendicular bisector to another line, what information would you need? BE SPECIFIC!

2) Algebraically determine if the line -x + y = 1 is the perpendicular bisector of AB, where A is (5,7), and B

is (6,6).

3) Write the equation of the perpendicular bisector of GH, given that G(2,-1) and H(10, -3).

a) Find the slope of GH.

b) What is the slope of a line perpendicular to GH? How did you find this answer?

c) Find the midpoint of GH.

d) Use the midpoint from (c) and the slope from (b) to write the equation of the perpendicular

bisector.

4) Write the equation of the perpendicular bisector of AB, given that A(5,-8) and B(-2,13).

5) In circle O, diameter RS has endpoints R(3a, 2b -1) and S(a-6, 4b+5).

a) Find the coordinates of point O, the center of the circle, in terms of a and b in simplest form.

b) Determine the slope of diameter RS.

6) The line of reflection is the same as the __________ _____________ between

an image and its corresponding pre-image

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Unit 3 (Part 1 of 2): Lines (Lessons 3-1 through 3-7) · Special Types of Linear Graphs Horizontal Lines Horizontal lines only travel through the y-axis, no x-intercept here! Equation: