1.6 Midpoint and Distance in the Coordinate Plane.notebook
August 22, 2016
In your foldable (formulas section)
For coordinates
A(x1, y1), B(x2, y2), & midpoint M(xm, ym)
The length of AB (or the distance from point A to point
B) can be found by using:
A
The distance formula
c
2
2
AB = √(x2 - x1) + (y2 - y1)
b
or
B
C
a
The Pythagorean Theorem
AB2 = AC2 + BC2
c2 = a2 + b2
The midpoint of AB can be found by using the midpoint
formula:
x2 + x1 y2 + y1
M(xm, ym) =
2
2
,
(
)
When given one endpoint and the midpoint of a
segment, we find the other endpoint using formula:
xm = x2 + x1 ym = y2 + y1
2
2
,
1
1.6 Midpoint and Distance in the Coordinate Plane.notebook
August 22, 2016
What we will learn today:
~ To develop & apply the formula for
midpoint, and
~ To use the Distance Formula & the
Pythagorean Theorem to find the
distance between two points.
Midpoint in the coordinate plane
Example 1 ~ Find the midpoint of a segment with
endpoints A(2, 0) and B(-8, 14)
Example 2 ~ Point M is the midpoint of AB. The
coordinates of A and M are given. Find the
coordinates of B.
(a) A(2, 7), M(6, 1)
(b) A(-8, 3), M(2, 5)
2
1.6 Midpoint and Distance in the Coordinate Plane.notebook
August 22, 2016
Example 3 ~ Find FG & JK. Then determine whether
~ JK.
FG =
Example 4 ~
(a) Use the Pythagorean Theorem to find DE.
(b) Use the Pythagorean Theorem to find RS.
3
1.6 Midpoint and Distance in the Coordinate Plane.notebook
August 22, 2016
Problem Solving Application
A player throws the ball
from first base to a point
located between third
base and home plate and
10 feet from third base.
What is the distance of
the throw, to the nearest
tenth?
4