1-6
Midpoint and Distance
in the Coordinate Plane
Why learn this?
You can use a coordinate plane to help
you calculate distances. (See Example 5.)
Objectives
Develop and apply the
formula for midpoint.
Use the Distance Formula
and the Pythagorean
Theorem to find the
distance between
two points.
Vocabulary
coordinate plane
leg
hypotenuse
Major League baseball fields are laid out
according to strict guidelines. Once you
know the dimensions of a field, you can
use a coordinate plane to find the distance
between two of the bases.
A coordinate plane is a plane that is
divided into four regions by a horizontal
line (x-axis) and a vertical line (y-axis).
The location, or coordinates, of a point
are given by an ordered pair (x, y).
You can find the midpoint of a segment by using the coordinates of its
endpoints. Calculate the average of the x-coordinates and the average of
the y-coordinates of the endpoints.
Midpoint Formula
_
The midpoint M of AB with
endpoints A(x 1, y 1) and B(x 2, y 2)
is found by
(
Preparation for
17.0
Students prove theorems by using
coordinate geometry, including
the midpoint of a line segment,
the distance formula, and various
forms of equations of lines and circles.
Also covered: 15.0
EXAMPLE
To make it easier to
picture the problem,
plot the segment’s
endpoints on a
coordinate plane.
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x1 + x2 _
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Finding the Coordinates of a Midpoint
−−
Find the coordinates of the midpoint of CD
with endpoints C(-2, -1) and D(4, 2).
y + y2
x1 + x2 _
M _
, 1
2
2
(
)
( )
1
= (1, _
2)
-2 + 4 _
-1 + 2
2, _
1
_
,
= _
2
2
2 2
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1. Find the coordinates of the midpoint of EF with endpoints
E(-2, 3) and F(5, -3).
1- 6 Midpoint and Distance in the Coordinate Plane
43