Coordinate Midpoint
Algebra Review
Homework: page 36-37/ 1-8
Midpoint of a Segment

Example 1:
Find the coordinates of M, the midpoint of
for G(8, –6) and H(–14, 12).
Answer: midpoint (–3, 3)
,
Your Turn:
a. Find the coordinates of the midpoint of
for X(–2, 3) and Y(–8, –9).
Answer: (–5, –3)
More About Midpoints
You can also find the
coordinates of an endpoint of a
segment if you know the
coordinates of the other
endpoint and its midpoint.
Example 2:
Find the coordinates of D if E(–6, 4) is the midpoint
of
and F has coordinates (–5, –3).
Let F be
in the Midpoint Formula.
Write two equations to find the coordinates of D.
Example 2:
Solve each equation.
Multiply each side by 2.
Add 5 to each side.
Multiply each side by 2.
Add 3 to each side.
Answer: The coordinates of D are (–7, 11).
Your Turn:
Find the coordinates of R if N(8, –3) is the midpoint
of
and S has coordinates (–1, 5).
Answer: (17, –11)
Example 3:
Multiple-Choice Test Item
What is the measure of
if Q is the midpoint of
A
B4
C
D9
?
Example 3:
Read the Test Item
You know that Q is the midpoint of
, and the figure gives
algebraic measures for
and
. You are asked to find
the measure of
.
Solve the Test Item
Because Q is the midpoint, you know that
.
Use this equation and the algebraic measures to find a
value for x.
Example 3:
Definition of midpoint
Distributive Property
Subtract 1 from each side.
Add 3x to each side.
Divide each side by 10.
Example 3:
Now substitute
for x in the expression for PR.
Original measure
Simplify.
Answer: D
Your Turn:
Multiple-Choice Test Item
What is the measure of
if B is the midpoint of
A1
Answer: B
B3
C5
D 10
?
Practice Problems
1. Find the midpoint between the points A(6,4) and B(3,-4).
A. (4.5, 4)
Incorrect. Look at your y-coordinate. You
added 4 and (-4) as 8, not 0.
B. (3, 0)
Incorrect. Look at your x-coordinate. You
divided 9 by 3 instead of 2.
C. (1.5, 4)
Incorrect. Look at your x- and y-coordinates. Check your
addition and subtraction.
A
D. (4.5, 0)
Correct. Great Job!
B
2. The endpoints of a line segment are the points with
coordinates (2,1) and (8,9). What are the coordinates of
the midpoint of the line segment?
A. (2, 3.5)
Incorrect. Double check the coordinates again.
B. (3, 4)
Incorrect. Make sure you are adding the coordinates, not subtracting them.
C. (5, 5)
Correct. Well done!
D. (10, 10)
Incorrect. Don’t forget to divide the sum of the coordinates by 2.
3. You are standing on the point (-4, 6) and your friend is
standing on the point (2, 5). You want to walk towards
each other and meet halfway. Find the point at which
you would meet.
A. (-1. 5.5)
Correct.
B. (-2, 6)
Incorrect. Take a look at both coordinates. Make sure you added
and subtracted correctly.
C. (0, 5.5)
Incorrect. Take a look at the x-coordinate.
D. (3, 5.5)
A.Incorrect. Take a look at the x-coordinate.
You
Your Friend
4. You are given the endpoint of a line segment C(1,2)
and its midpoint D(3,1). What is the other endpoint?
A. (5,2)
Incorrect. This point does not lie in a straight line with the other points.
B. (6,0)
Close! Check the coordinates again.
C. (5,0)
Correct!
D. (-1,3)
Incorrect. D, not C should be the midpoint.
C
D
5. Find the coordinates of the endpoint K if L(-2, -5) is the
midpoint of and the coordinates of N are (6, 7).
A. (-10, -17)
Correct!
B. (10, 17)
Incorrect. Check that you have L as the midpoint.
C. (-2, 17)
Incorrect. Check your x-coordinate and double check that
your y-coordinate in the right direction.
D. (-2, -3)
Incorrect. Look at the placement of this point. Does it make
sense for this to be the endpoint in relation to the other two
points?
6. If A(2,4) and B(6,4) are the endpoints of a diameter of a
circle, find the coordinates of the center of the circle.
A. (3,4)
Incorrect. Check your x-coordinate. Make sure you
add both the 6 and 2.
B. (4,4)
Correct!
C. (4,5)
Incorrect. Check your y-coordinate.
D. (8,8)
Incorrect. Don’t forget to divide the coordinates by 2 after you
add them.
7. You are standing at the point (0,0) and your friend is
standing at the point (4,2). You are going to deliver a
message to her and you want to meet her halfway. At what
point will you meet?
A. (2,0)
Incorrect. 2 is halfway between the x-coordinates, but what is
halfway between the y-coordinates?
B. (2,1)
Correct!
C. (4,1)
Incorrect. 1 is the correct midpoint in the y-direction, but
double check the midpoint in the x-direction.
D. (2,2)
Incorrect. Double check your y-coordinate.
Additional Practice Problems
Practice 1: Finding the Coordinates of a Midpoint
Find the coordinates of the midpoint M of PQ
with endpoints P(–8, 3) and Q(–2, 7).
M = (–5, 5)
Practice 2: Finding the Coordinates of a
Midpoint
Find the coordinates of the midpoint M of EF
with endpoints E(–2, 3) and F(5, –3).
Practice 3: Finding the Coordinates of an Endpoint
M is the midpoint of XY. X has coordinates
(2, 7) and M has coordinates (6, 1). Find
the coordinates of Y.
Step 1 Let the coordinates of Y equal (x, y).
Step 2 Use the Midpoint Formula:
Practice 3 Continued
Step 3 Find the x and y –coordinates of the endpoint
Y by solving each equation.
Set the coordinates equal.
Multiply both sides by 2.
12 = 2 + x
– 2 –2
Simplify.
Subtract.
10 = x
Simplify.
The coordinates of Y are (10, –5).
2=7+y
– 7 –7
–5 = y
Practice 4: Finding the Coordinates of an Endpoint
S is the midpoint of RT. R has coordinates
(–6, –1), and S has coordinates (–1, 1).
Find the coordinates of T.
Step 1 Let the coordinates of T equal (x, y).
Step 2 Use the Midpoint Formula:
Practice 4 Continued
Step 3 Find the x-coordinate.
Set the coordinates equal.
Multiply both sides by 2.
–2 = –6 + x
+ 6 +6
4=x
Simplify.
Add.
2 = –1 + y
+1 +1
Simplify.
3=y
The coordinates of T are (4, 3).