1. 1.7 Midpoint and Distance in the Coordinate Plane
SOL: G3a
Objectives: TSW …
To find the midpoint of a segment.
To find the distance between two points in the
coordinate plane.

2. Midpoint
the point that divides the segment into two congruent () segments.
If X is the midpoint of AB, then AX  XB and AX = XB A B X
Midpoint

3. How do we find the Midpoint
If we have a Number Line, then we use the two endpoints, add them together and divided by two. P Q a b M
a + b 2
Midpoint =

4. Example 1: Finding the Midpoint
The coordinates on a number line of J and K are
–12 and 16, respectively. Find the coordinate of
the midpoint of JK. K J
-12 16 2 4 2 =
Midpoint =
= 2

5. Example 2: Finding the Midpoint
MN has the endpoints at -9 and 4. What is the coordinate of its midpoint? N M -9 4
-9 + 4 2 -5 2 =
Midpoint =
= -2 ½

6. Midpoint Formula: If we are working in the Coordinate Plane
When using the midpoint formula you can use the points in any order, remember addition is commutative.

7. ( , ) ( , ) Example 3: Find the coordinates of the midpoint of GH for
G(8, -6) and H(-14, 12).
( , )
( , ) -6 2 6 2 2 2
Midpoint = =
= (-3, 3)

8. ( , ) ( , ) Example 4: Find the coordinates of the midpoint of RS for
R(5, -10) and S(3, 6).
( , )
( , ) 8 2 -4 2
5 + 3 2 2
Midpoint = =
= (4, -2)

9. Example 5: Find the missing endpoint
Find the coordinates of D if E(-6, 4) is the midpoint of DF and F has coordinates (5, -3).
( , )
5 + x 2
-3 + y 2
(-6, 4) =
5 + x 2
-3 + y 2
-6 =
4 =
-12 = 5 + x
8 = -3 + y
(-17, 11) =
-17 = x
11 = y

10. Example 6: PQ = QR = 6 – 3x (6 – 3x) + (6 – 3x) = 14x + 2 10 = 20x
What is the measure of PR if Q is the midpoint of PR?
PQ = QR = 6 – 3x
(6 – 3x) + (6 – 3x) = 14x + 2
10 = 20x
12 – 6x = 14x + 2
+ 6x + 6x
½ = x
12 = 20x + 2
PR = 14x + 2
= 14(½) + 2
10 = 20x
= 9

11. Distance Formula – Coordinate Plane to find Distance
The distance d between two points with coordinates (x1, y1) and (x2, y2) is given by
Based on the Pythagorean Theorem, which we will learn about later.

12. Example 7: What is the distance?
Find the distance between E(-4, 1) and F(3, -1)
EF = (-4 – 3)2 + (1 +1)2
EF =
EF = 53
EF ≈ 7.28

13. Example 8: What is the distance?
Find the distance between S(-2, 14) and R(4, 3)
SR = (-2 – 4)2 + (14 - 3)2
EF =
EF = 180
EF ≈