This document provides formulas and examples for calculating the distance and midpoint between two points. The distance formula is used to find the distance between two points (x1, y1) and (x2, y2). The midpoint formula finds the midpoint between two points by taking the average of the x-coordinates and y-coordinates. Several examples demonstrate using the distance and midpoint formulas to find distances, midpoints, and missing endpoint coordinates. The key steps are to work inside parentheses, do exponents before addition, and plug points into the formulas.

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