Midpoint Formula

Show your work for each problem.

1.
What is the midpoint of a segment with endpoints and ?
1. a)
2. b)
3. c)
4. d)
Answer:
Using the midpoint formula:
2.
Find the x-coordinate of the midpoint of a segment with endpoints and .
Answer: 6
3.
The midpoint formula finds the ___ of the coordinates.
1. a)difference
2. b)sum
3. c)product
4. d)average
Answer: average
The midpoint formula averages the coordinates: is the average of and .
4.
Find the midpoint of the segment with endpoints and .
Answer: (3, 5)
1. What is the average of the x-coordinates? 3
2. What is the average of the y-coordinates? 5
3. Write the midpoint as an ordered pair . (3, 5)
5.
Find the y-coordinate of the midpoint of a segment with endpoints and .
Answer: 5
6.
What is the midpoint of the segment with endpoints and ?
1. a)
2. b)
3. c)
4. d)
Answer:
7.
Find the midpoint of the segment with endpoints and . Write your answer as .
Answer: (2, -1)
8.
Find the midpoint of the segment with endpoints and .
Answer: (2, 2)
1. Add the x-coordinates: 4
2. Divide by 2 to get : 2
3. Add the y-coordinates: 4
4. Divide by 2 to get : 2
5. Write the midpoint as . (2, 2)
9.
The midpoint of segment is . If , what is ?
1. a)
2. b)
3. c)
4. d)
Answer:
Solving gives . Solving gives . So .
10.
A segment has midpoint and one endpoint . Find the other endpoint .
Answer: (7, -1)
1. Set up the equation for x: . Solve for . 7
2. Set up the equation for y: . Solve for . -1
3. Write point as an ordered pair. (7, -1)
11.
What is the midpoint of the segment with endpoints and ? Write your answer as .
Answer: (4, -2)
12.
The midpoint of segment is . If , find point .
Answer: (-7, 9)
1. Write the equation for : -2
2. Multiply both sides by 2: -4
3. Solve for : -7
4. Write the equation for : . Solve for . 9
5. Write point as an ordered pair. (-7, 9)
13.
Point is the midpoint of . If , what is ?
1. a)
2. b)
3. c)
4. d)
Answer:
. . So .
14.
Find the midpoint of the segment with endpoints and . Write your answer as .
Answer: (-3, 2)
15.
A rectangle has vertices at , , , and . Find the coordinates of the center of the rectangle.
Answer: (4, 3)
1. The center is the midpoint of diagonal . What are the endpoints? A(0,0) and C(8,6)
2. Find the x-coordinate of the center: 4
3. Find the y-coordinate of the center: 3
4. Write the center as an ordered pair. (4, 3)