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Apply the Distance & Midpoint formulas
Find the distance and the midpoint
Find the missing endpoint
Formulas:
2 22 1 2 1( ) ( )d x x y y
2 1midpoint2
x xx
2 1
midpoint2
y yy
midpoint midpoint( , )x y
Distance formula:
Midpoint formula:
Ex 1Find the distance between the points P(-3, 2) and Q (-2, 4).
1, 1( )x y 2, 2( )x y
2 22 1 2 1( ) ( )d x x y y
2 2( ) ( )d 2 3 24
2 2( ) ( )d 1 2
d 1 4
5 d
Work inside parentheses
Do powers before doing the addition!!!!!!
Ex 2Find the distance between the points P(-5, 3) and Q (4, 5).
1, 1( )x y 2, 2( )x y
2 22 1 2 1( ) ( )d x x y y
2 2( ) ( )d 4 5 35
2 2( ) ( )d 9 2
d 81 4
85 d
Work inside parentheses
Do powers before doing the addition!!!!!!
Ex 3Find the distance between the points P(-2, -5) and Q (-1, 3).
1, 1( )x y 2, 2( )x y
2 22 1 2 1( ) ( )d x x y y
2 2( ) ( )d 1 2 53
2 2( ) ( )d 1 8
d 1 64
65 d
Work inside parentheses
Do powers before doing the addition!!!!!!
Ex 4
2 1midpoint2
x xx
2 1midpoint2
y yy
midpoint midpoint( , )x y
Find the midpoint whose endpoints are (2, -3) and (-14, 13)1, 1( )x y 2, 2( )x y
midpoint
2x
14 2
212
6
( , )6
midpoint
2y
13 3
210
5
5
Ex 5
2 1midpoint2
x xx
2 1midpoint2
y yy
midpoint midpoint( , )x y
Find the midpoint whose endpoints are (1, -2) and (-17, 16)1, 1( )x y 2, 2( )x y
midpoint
2x
17 1
216
8
( , )8
midpoint
2y
16 2
214
7
7
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 102 2
1y 12
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 42 2
1y 6
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 148 8
1y 6
