1.5 – Midpoint

Midpoint:

Point in the middle of a segment

A BM

MBAM

Ex 1: Find the midpoint of the segment.

M M

1 -1

Ex 2: Find the midpoint of the numbers without a number line. a. 10 and 150

b. 34 and 72

c. How did you find the midpoint?

10+1502

= 80

34+722

= 53

Added them and then divided by 2

Ex 3: Find the midpoint of AB using a coordinate plane. a. A(5, 6) and B(1, 2)

A(5, 6)

M( , )

B(1, 2)

A

B

M

3 4

b. A(–5, 6) and B(1, –2)

A(-5, 6)

M( , )

B(1, -2)

A

B

M

-2 2

c. Look and compare the x-coordinates then compare the y-coordinates. How can you find the midpoint of any segment without drawing a graph?

Add the x’s then divide by 2

Add the y’s then divide by 2

Midpoint Formula:

1 2 1 2,2 2

x x y y

Ex 4: Use the formula to find the midpoint of A(–4, 3) and B(–8, –9).

x1 y1 x2 y2

4 8,

2

3 9

2

6, 3

Ex 5: Given the midpoint, M, of the segment, find the indicated measures.

a.

 MZ = ___________ 

x + 2 = 2x – 3

2 = x – 3

5 = x

2(5) – 3= 7

b.

PR = ___________

5x – 7 = 3x + 1

2x – 7 = 1

2x = 8

x = 4

5(4)-7 =13 13

13+13 = 26

Ex 6: Given the midpoint and one endpoint, find the other endpoint.

A ( , )M

B

A

M (2 , 1)

B (1, 4)

3 -2

A (4, 4)

M (-1, -2)

B ( , )-6 -8

A ( , )

M (6 , 5)

B (7, 8)

5 2

A (-1, 2)

M (1, 0)

B ( , )3 -2