Distance and Midpoint Formulas Activity
Name________________________
Distance Formula: The distance between two points is: d  ( x  x ) 2  ( y  y ) 2
2 1
2
1
 ( x  x1 y 2  y1 
Midpoint Formula: The midpoint (middle) of the line between two points is:  2
,

2 
 2
Examples:
1.) Find the distance between the two points.
2.) Find the midpoint of
P(-3, -2) and Q(5, -2).
3.) Find the distance between the two points.
P(7, 0) and Q(8 , 0)
4.) Find the midpoint of the two
points. P(-3, -4) and Q(5, -5)
Practice Problems:
5.) For PQ the coordinates of P and Q are given below. Find the distance of this segment.
P(-2, 3) and M (5, 1)
d=
6.) For PQ the coordinates of P and Q are given below. Find the midpoint of this segment.
P(3, 11) and M (0, 0)
m=
7.) Find the distance and midpoint for the following coordinates.
P(7.6 , 10.1) and Q(4.6 , 3.1)
d=
m=
8.) Find the distance and midpoint for the following coordinates.
P(10, 2) and Q(8, 0)
d=
m=
Example:
9.) Determine the coordinates of the points needed. Then find the distance of each line
segment (round to nearest tenth if necessary):
Practice:
10.) Triangle ABC has coordinates A (2, 4), B (-4,3) and C (1, -5). D is the midpoint of AB and E is the
midpoint of AC.
a) Graph the points A, B, and C (make sure you label
them). Find the coordinates of points D and E. Show
all work.
d=
E=
b) Find the distance of AB and AC:
AB=
AC=
Homework:
Page 479-480
#’s 4-26 evens and 39