Write the equation of the line:1. Parallel (∥) to 8x – 2y = 6

and goes through (5, -2) in Standard form

Warm up

MidpointGiven 2 ordered pairs,

it’s theAVG of the x’s and

AVG of the y’s.

Midpoint Formula

1 2 1 2,2 2

x x y y

Find the midpoint.

1. (3, 7) and (-2, 4)

2. (5, -2) and (6, 14)

(.5, 5.5)

(5.5, 6)

Find the midpoint.

3. (3, -9) and (14, 16)

4. (12, 17) and (-7, 9)

(8.5, 3.5)

(2.5, 13)

Find the midpoint.5.

(2, 3)

Find the midpoint.6.

(1.5, 4)

Given the midpt and one endpt, find the other endpt.

7. Midpt (3, -6) Endpt (7, -3)

(-1, -9)

Given the midpt and one endpt, find the other endpt.

8. Midpt (-1, 2) Endpt (3, 0)

(-5, 4)

Given the midpt and one endpt, find the other endpt.

9. Midpt (-4, 6) Endpt (2, 1)

(-10, 11)

Partition Line Segments(1 Dimension)

2 1 1( )

ax x xa b

Partition – 1 Dimension

A is at 1, and B is at 7.Find the point, T, so that T partitions A to B in a 2:1 ratio.

Partition – 1 Dimension

A is at -6 and B is at 4.Find the point, T, so that T is A to B in a 2:3 ratio.

Find a Point that Partitions a Segment in a

Given Ratio a:b

2 1 1 2 1 1,a ax x x y y ya b a b

Find the coordinates of P along the directed line segment AB so that the ratio of AP to PB is 3 to 2.

In order to divide the segment in the ratio of 3 to 2, think of dividing the segment into 3 + 2 or 5 congruent pieces.

A(3, 4), B(6, 10); 3 to 2.

AB has a rise of 6.

6

AB has a run of 3.

3

A(3, 4), B(6, 10); 3 to 2.

To find the coordinates of point P…

6

3

1 1, a arun x rise ya b a b

3 33 3, 6 45 5

4.8, 7.6

Example 1: Find the coordinates of point P along the directed line segment AB so that AP to PB is the given ratio. A(1, 3), B(8, 4); 4 to 1.

2 1 1 2 1 1, a ax x x y y ya b a b

4 47 1, 1 35 5

6.6, 3.8

Example 2: Find the coordinates of point P along the directed line segment AB so that AP to PB is the given ratio. A(-2, 1), B(4, 5); 3 to 7.

2 1 1 2 1 1, a ax x x y y ya b a b

3 36 2, 4 110 10

0.2, 2.2

Example 3: Find the coordinates of point P along the directed line segment AB so that AP to PB is the given ratio. A(8, 0), B(3, -2); 1 to 4.

2 1 1 2 1 1, a ax x x y y ya b a b

1 15 8, 2 05 5

7, 0.4

Example 4: Find the coordinates of point P along the directed line segment AB so that AP to PB is the given ratio. A(-2, -4), B(6, 1); 3 to 2.

2 1 1 2 1 1, a ax x x y y ya b a b

3 38 2, 5 45 5

2.8, 1

HomeworkPartitioning Segments Worksheet