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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