Geo 1­3.notebook
August 24, 2012
1-3, Distance and Midpoints
Today you will...
- Find the distance between two points.
- Find the midpoint of a segment.
Distance Between Two Points
The distance between two points is the length of the segment with
those points as its endpoints.
The order in which you name the endpoints is not important when
calculating distance.
To find the distance between two points in the coordinate plane, you
can form a right triangle.
Recall that the Pythagorean Theorem is often expressed as a 2 + b2 = c2
where a and b are the measures of the shorter sides (legs) and c is the
measure of the longest side (hypotenuse).
Geo 1­3.notebook
August 24, 2012
Distance Formula (in Coordinate Plane)
Find the distance between each pair of points.
E (-5, 6) and F (8, -4)
J(4, 3) and K(-3, -7)
Midpoint of a Segment
Midpoint Formula (in a Coordinate Plane)
The midpoint of a segment is the point halfway between the endpoints
of the segment. You can find the midpoint of a segment on a number
line by finding the mean, or the average, of the coordinates of its
endpoints.
You can find the midpoint of a segment on the coordinate plane by
finding the average of the x-coordinates and of the y-coordinates of
the endpoints.
Find the coordinates of the midpoint of a segment with the given
coordinates.
You can also find the coordinates of the endpoint of a segment if you
know the coordinates of its other endpoint and its midpoint.
A(5, 12) and B(-4, 8)
C(-8, -2) and D (5, 1)
To do this, we use the midpoint formula and work backward!
Geo 1­3.notebook
August 24, 2012
Find the coordinates of the missing endpoint if P is the midpoint of EG.
E(-8, 6) and P(-5, 10)
P(-1, 3) and G(5, 6)
You can use algebra to find a missing measure or value in a figure that
involves the midpoint of a segment.