Distance and Midpoint

1. Apply the Distance &
Midpoint formulas
Find the distance and the midpoint
Find the missing endpoint

2. Formulas:
2 2
2 1 2 1( ) ( )d x x y y= − + −
2 1
midpoint
2
x x
x
+
= 2 1
midpoint
2
y y
y
+
=
midpoint midpoint( , )x y
Distance formula:
Midpoint formula:

3. Ex 1
Find the distance between the points P(-3, 2) and Q (-2, 4).
1, 1( )x y 2, 2( )x y
2 2
2 1 2 1( ) ( )d x x y y= − + −
2 2
( ) ( )d = − + −2− 3− 24
2 2
( ) ( )d = +1 2
d = +1 4
5d =
Work inside
parentheses
Do powers before
doing the
addition!!!!!!

4. Ex 2
Find the distance between the points P(-5, 3) and Q (4, 5).
1, 1( )x y 2, 2( )x y
2 2
2 1 2 1( ) ( )d x x y y= − + −
2 2
( ) ( )d = − + −4 5− 35
2 2
( ) ( )d = +9 2
d = +81 4
85d =
Work inside
parentheses
Do powers before
doing the
addition!!!!!!

5. Ex 3
Find the distance between the points P(-2, -5) and Q (-1, 3).
1, 1( )x y 2, 2( )x y
2 2
2 1 2 1( ) ( )d x x y y= − + −
2 2
( ) ( )d = − + −1− 2− 5−3
2 2
( ) ( )d = +1 8
d = +1 64
65d =
Work inside
parentheses
Do powers before
doing the
addition!!!!!!

6. Ex 4
2 1
midpoint
2
x x
x
+
=
2 1
midpoint
2
y y
y
+
=
midpoint midpoint( , )x y
Find the midpoint whose endpoints are (2, -3) and (-14, 13)
1, 1( )x y 2, 2( )x y
midpoint
2
x
+
=
14− 2
2
=
12−
6−
( , )6−
midpoint
2
y
+
=
13 3−
2
=
10
5
5

7. Ex 5
2 1
midpoint
2
x x
x
+
=
2 1
midpoint
2
y y
y
+
=
midpoint midpoint( , )x y
Find the midpoint whose endpoints are (1, -2) and (-17, 16)
1, 1( )x y 2, 2( )x y
midpoint
2
x
+
=
17− 1
2
=
16−
8−
( , )8−
midpoint
2
y
+
=
16 2−
2
=
14
7
7

8. Ex 6
M(-3, -5) is the midpoint of RS. If S has a coordinates (-2, 2),
find the coordinates of R.
2, 2( )x y
2
+
=
2− 1x
12 x− + = 6−
( , )4−
2
+
=
2 1y
12−
,( )m mx y1, 1( )x y
R (x1, y1) S (-2, 2)M(-3, -5)
3−
5−(2) (2)
2+ 2+
1x = 4−
(2) (2)
12 y+ = 10−
2− 2−
1y = 12−

9. 7 ExM(4, 2) is the midpoint of RS. If S has a coordinates (5, -2),
find the coordinates of R.
2, 2( )x y
2
+
=
5 1x
15 x+ = 8
( , )3
2
+
=
2− 1y
6
,( )m mx y1, 1( )x y
R (x1, y1) S (5,-2)M(4, 2)
4
2(2) (2)
5− 5−
1x = 3
(2) (2)
12 y− + = 4
2+ 2+
1y = 6

10. Ex 8
M(-8, 7) is the midpoint of RS. If S has a coordinates (-6, 8),
find the coordinates of R.
2, 2( )x y
2
+
=
6− 1x
16 x− + = 16−
( , )10−
2
+
=
8 1y
6
,( )m mx y1, 1( )x y
R (x1, y1) S (-6, 8)M(-8, 7)
8−
7(2) (2)
6+ 6+
1x = 10−
(2) (2)
18 y+ = 14
8− 8−
1y = 6