Geom.–Ch.1.6AMidpointFormula

Mr.Deyo

HomeWork1‐2‐3:1)StormCheckPastedinNotebook?

2)Section______ 3)Section______RFM/RTProblems_________ NotesCopiedinNotebook?Pasted&SolvedinNotebook?

Students will apply the midpoint formula to find midpoint and endpoints of a segment.

Students will demonstrate this by completing a graphic organizer and by solving problems in a pair activity.

Learning Target

Storm Check (Think, Write, Discuss, Report) Questions on which to ponder and answer: 1.  How are the two images similar? 2.  How are they different? 3.  How can these two images be related to math?

1) Midpoint2) Distance3) Hypotenuse4)  Leg

Vocabulary

1.  Teachersaystheword.•  ALLStudentsrepeattheword.

2.  Teachercountsoutsyllablesass/hesaystheword.

•  ALLstudentsrepeatsyllablecountastheysaytheword.

3.  Studentteamscreateaphysicalrepresentationoftheword.

•  ClasschoosesonephysicalrepresentationforALLstudents.

4.  Studentteamscreateafriendlydefinitionfortheword.

•  Classchoosesonefriendlydefinitionfortheword.

DAY 3 and/or DAY 4 1. Review the word

♦ Friendly Definition ♦ Physical Representation

2. Show how the word works ♦ Synonyms/antonym ♦ Word Problems ♦ Related words/phrases ♦ Example/non-example

Friendly Definition Sketch

Wordwork Sentence

DAY 2 1. Review word

♦ Friendly Definition ♦ Physical Representation

2. Draw a sketch

DAY 5 1. Review the word

♦ Friendly definition ♦ Physical Representation

3. Write a sentence  at least 2 rich words (1 action)  correct spelling  correct punctuation  correct subject/predicate agreement  clear and clean writing

DAY 1 1.  Use Visuals

2.  Introduce the word ♦ Friendly Definition ♦ Physical Representation

3.  Use Cognates

4.  Write friendly definition

5.  Physical Representation

WordList1.  2.  3.  4. 

Notes: A coordinate plane is a plane that is divided into four regions by a horizontal line (x-axis) and a vertical line (y-axis) . The location, or coordinates, of a point are given by an ordered pair (x, y). You can find the midpoint of a segment by using the coordinates of its endpoints. Calculate the average of the x-coordinates and the average of the y-coordinates of the endpoints.

A‐BProblemAnotes:

Find the coordinates of the midpoint of EF with endpoints E(–2, 3) and F(5, –3).

A‐BProblemACheck:

Find the coordinates of the midpoint of EF with endpoints E(–2, 3) and F(5, –3).

A‐BProblemBSOLVE!!

Find the coordinates of the midpoint of PQ with endpoints P(–8, 3) and Q(–2, 7).

A‐BProblemBCheck!!

Find the coordinates of the midpoint of PQ with endpoints P(–8, 3) and Q(–2, 7).

= (–5, 5)

StormCheck(Think,Write,Discuss,Report)

Withoutdoingcalculations,givemetwoexamplesinyourlifewhereyouwanttofindthemidpointofsomething?

Inmyownlife,Itrytofindthemidpointwhen

_______________________________________

andwhen_______________________________

_______________________________________.

A‐BProblemAnotes: Finding the Coordinates of an Endpoint

M is the midpoint of LN. L has coordinates (2, 7) and M has coordinates (6, 1). Find the coordinates of N. Step 1 Let the coordinates of N equal (x, y). Step 2 Use the Midpoint Formula:

L NM(6, 1)(2, 7) (x, y)

TakeHalfofFormulaandSolveforX TakeHalfofFormula&SolveforY

( , )

A‐BProblemACheck:

Step 3 Find each coordinate separately.

Setthecoordinatesequal.

Multiplybothsidesby2.

12 = 2 + x Simplify.

– 2 –2

10 = x

Subtract.

Simplify.

– 7 –7

The coordinates of N are

–5 = y

2 = 7 + y

L NM(6, 1)(2, 7) (x, y)

(10,-5)

A‐BProblemBSOLVE!!S is the midpoint of RT. R has coordinates (-6,-1) and S has coordinates (-1, 1). Find the coordinates of T. Step 1 Let the coordinates of T equal (x, y). Step 2 Use the Midpoint Formula:

R TS(-1, 1)(-6,-1) (x, y)

TakeHalfofFormulaandSolveforX TakeHalfofFormula&SolveforY

( , )

A‐BProblemBCheck!!Step 3 Find the x-coordinate.

Setthecoordinatesequal.

Multiplybothsidesby2.

–2 = –6 + x Simplify.

+ 6 +6

4 = x

Add.

Simplify.

+ 1 + 1

3 = y

The coordinates of T are

L NM(-1, 1)(-6, -1) (x, y)

(4,3)

2 = –1 + y

StormCheck(Think,Write,Discuss,Report)

Whenyouusethemidpointformulatosolveforamidpointoranendpoint,howdoyouusethesameformuladifferentlyineachcase?

Whensolvingforamidpoint,_______________

_______________________________________

Whensolvingforanendpoint,______________

_______________________________________.

1) Midpoint2) Distance3) Hypotenuse4)  Leg

Vocabulary Review

1.  Teachersaystheword.•  ALLStudentsrepeattheword.

2.  Teachercountsoutsyllablesass/hesaystheword.

•  ALLstudentsrepeatsyllablecountastheysaytheword.

3.  Studentteamscreateaphysicalrepresentationoftheword.

•  ClasschoosesonephysicalrepresentationforALLstudents.

4.  Studentteamscreateafriendlydefinitionfortheword.

•  Classchoosesonefriendlydefinitionfortheword.

Students will apply the midpoint formula to find midpoint and endpoints of a segment.

Students will demonstrate this by completing a graphic organizer and by solving problems in a pair activity.

Learning Target

Ticket OUT.

1. Find the coordinates of the midpoint of MN with endpoints M(-2, 6) and N(8, 0).

2. K is the midpoint of HL. H has coordinates (1, –7), and K has coordinates (9, 3). Find the coordinates of L.

HomeWork1‐2‐3:1)StormCheckPastedinNotebook?

2)Section______ 3)Section______RFM/RTProblems_________ NotesCopiedinNotebook?Pasted&SolvedinNotebook?

TO 2) (17, 13) TO 1) (3, 3)