The Algebra Teacher\'s Guide to Reteaching Essential Concepts and Skills

Name Date

WORKSHEET 4.15: USING THE MIDPOINT FORMULA

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A midpoint is a point on a line segment located exactly between the two endpoints. The

midpoint between two points,(x 1 ,y 1 )and(x 2 ,y 2 ), can be found by using the midpoint formula:

(

x 1 +x 2

2

,

y 1 +y 2

2

)

. Follow the steps below to find the midpoint between two points:

1. Determine which ordered pair will represent(x 1 ,y 1 )and which will represent(x 2 ,y 2 ).


2. Replace each variable in the midpoint formula with the appropriatex-coordinates or
   y-coordinates.


3. Solve to find each value.

EXAMPLE

Find the midpoint between (2, 3) and (6, 7).

Label (2, 3) as(x 1 ,y 1 )and (6, 7) as(x 2 ,y 2 ).

Replace each variable in the midpoint formula with the correct values:

(

2 + 6

2

,

3 + 7

2

)

.

The midpoint between (2, 3) and (6, 7) is (4, 5).

DIRECTIONS: Find the midpoint between each pair of points.

1. (3, 0), (4, 9) 2. (1, 2), (5, 8)


2. (−1, 2), (3, 4) 4.(−3,−6), (5, 3)

5.(−4,−1), (−8,−3) 6.(10,−9), (−9, 3)

7.(1, 7), (3, 7) 8.(0, 2), (1, 5)

CHALLENGE:Will’s dog took a bite out of his homework and he lost part of

his work. All that remained was the ordered pair (3, 4), the midpoint (6, 2),

and they-coordinate of 0 for the second ordered pair. Use the midpoint

formula to find the missingx-coordinate.

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2011 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla. All rights reserved.