Page 83 - Math Course 1 (Book 2)

Midpoints of a Segment

Solve each equation
Let’s Begin
X + (–5)
–6 = 1
2
–12 = X – 5 Multiply each side by 2.
Find Coordinates of Midpoint 1
–7= X Add 5 to each side.
1
Example y + (–3)
4 = 1
2
ALGEBRA 8 = y – 3 Multiply each side by 2.
1
The coordinates on a number line of J and K are 11 = y Add 3 to each side.
–12 and 16, respectively. Find the coordinate of the 1
midpoint of JK
Answer The coordinates of D are
Let M be the midpoint of JK (–7, 11).
–12 + 16
M = a = –12, b = 16
2
4
= or 2 Simplify.
2 Use Algebra to Find Measures

Answer 2 Example

Find the coordinates of M, the midpoint of GH, for What is the measure of PR if Q is the midpoint of
G (8, –6) and H (–14, 12).
PR?

Let G be (X , Y ) and H be (X , Y ).
1 1 2 2
X + X y + y
M ( 1 2 , 1 2 )
2 2
8 + (–14) –6 + 12
= M ( , ) You know that Q is the midpoint of PR, and the
2 2
f gure gives algebraic measures for QR and PR.
–6 6
= M ( , ) or M (–3, 3) You are asked to f nd the measure of PR.
2 2

1
Answer (–3, 3) Because Q is the midpoint, you know that QR = PR
2

Find the coordinates of D if E (–6, 4) is the midpoint Use this equation and the algebraic measures to
of DF and F has coordinates (–5, –3)
f nd a value for x.

Let F be ( x y ) in the Midpoint Formula. 1
2 2 QR = PR Def nition of midpoint
2
x +(–5) y +(–3) (X , Y ) 1
E(–6, 4) = E 1 , 1 2 2 6 – 3x = (14x + 2) QR = 6 – 3x, PR = 14 + 2
2
2 2 = (–5, –3)
Write two equations to f nd the coordinates of D. 6 – 3x = 7x+1 Distributive Property

x + (–5) y + (–3) 5 – 3x = 7x Subtract 1 from each side.
–6 = 2 4 = 1
2 2
5 = 10x Add 3x to each side.

1
= x Divide each side by 10.
2
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