Download 1-7 = Coordinate Geometry

You should remember the
basics of graphing from
algebra:
Many geometric
objects (segments,
angles, etc.) can be
graphed in the coordinate
plane, and we can use the
corresponding numbers to find
out information about them.
You already know how to find
the midpoint and the distance
between two endpoints of a
segment on a number line.
In this section we will expand
the ideas of midpoint and
distance to segments in the
coordinate plane.
Midpoint
 exact center of a segment
 halfway between the
endpoints
 To find the midpoint, you
literally average the
endpoints

𝑀=
𝑥1 +𝑥2 𝑦1 +𝑦2
,
2
2
Find the midpoint of (-2,4)
and (3,-1).
Find the midpoint of (-2,4)
and (3,-1).
(½,1½)
Find the midpoint of (-2,1) and
(4,3)
Find the midpoint of (-2,1) and
(4,3)
(1,2)
You can also use this rule to
find an endpoint.
Distance Formula
To find the distance between
two points ...
𝑑=
𝑥2 − 𝑥1
2
+ 𝑦2 − 𝑦1
2
𝑑=




𝑥2 − 𝑥1
2
+ 𝑦2 − 𝑦1
Subtract x’s, and square
Subtract y’s, and square
Add up
Take the square root
2
You may be familiar with the
Pythagorean Theorem. This
is really just another form of it.
Find the distance between
(1,2) and (5,5)
Find the distance between
(1,2) and (5,5)
5−1
2
+ 5−2
2
Find the distance between
(1,2) and (5,5)
5−1
2
+ 5−2
2
=5
Find the distance between
(-1,0)
and
(2,7)
Find the distance between
(-1,0)
and
(2,7)
2 − −1
2
+ 7−0
2
Find the distance between
(-1,0)
and
(2,7)
2 − −1 2 + 7 − 0
___
=  58  7.61577
2
REMEMBER …
 Midpoint Formula
 Distance Formula