S. Carbone Geometry Honors
Name
Section 1.6 Midpoint & Distance Formulas
Period
Date
Objective: Use the midpoint formula to find coordinates of midpoints/endpoints, and use the distance formula to
find the distance between two points.
1) What does it mean to find the average of two numbers? (ex: the average of 20 and 40)
2) In your own words, what is a midpoint?
3) On page 43 of your book you will find the midpoint formula. Write the midpoint formula and answer the
questions about the midpoint formula that follow.
(Midpoint) M =
a) What do you need to find a midpoint with the midpoint formula?
b) What are you finding when you sum the x-values and divide by two? When you sum the y-values and
divide by 2? (pg. 43)
4) Using the midpoint formula, find the midpoint of a segment that has endpoints with coordinates of (0, 5) and
(6, 5). (use example 1 on page 43 to help you through if you are stuck)
5) Verify that you did problem six correctly by plotting each point, then writing the coordinates of the midpoint
by visually locating the midpoint.
1
6) Sometimes you may not know the coordinates of both endpoints. You may only know coordinates for one
endpoint and the midpoint. In this situation you may plug in the values you know and solve for the
coordinates of the other endpoint. Page 44 example 2 illustrates this.
A (2,2)
M (4, -3)
B (?, ?)
The left side of example 2 in the book illustrates how to find the
x-cooridnate of the endpoint and the right side of the example
illustrates how to find the y-coordinate.
7) Using the midpoint formula find the endpoint for a segment that has one endpoint F(2, -2) and a midpoint at
T(2, 0). (use example 2 on page 44 to help you through the problem if you are stuck)
8) Use the grid in problem 5 on the worksheet to plot the endpoints and midpoint to verify your answer in
problem 7 from the worksheet.
2
Distance Formula
Simplify the following
1)
2)
24
Distance formula
3)
48
60
d=
4) Use the distance formula to find the distance between the points (1, -2) and (-4, -4). (use the example 3 or 4
on pages 44-45 to help you through if you are stuck)
5) Use the distance formula to find the distance between the points (-2, 7) and (-2, -8).
6) Plot the points from number five, then count the distance between the points to see if your solution is
10
correct.
8
6
4
2
-10 -8
-6
-4
-2
2
4
6
8
10
-2
-4
-6
-8
HW: p.47 #13, 15, 28, 34, 35, 36, 37,38,39,40
-10
3