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PIB Geometry
13-5: The Midpoint Formula
13-5 Warm Up
Given T(-5, -4), U(0, 1), V(4, 1), W(-4, -7),
decide what kind of quadrilateral TUVW
is, then prove it.
Homework 13-3 Questions?
• Turn in 13-2
13-5 Objectives
1. State, and apply the midpoint formula for
two points in a coordinate plane.
Theorem 13-5: The Midpoint Formula
The midpoint of the segment that joins two points
𝑥1 , 𝑦1 𝑎𝑛𝑑 𝑥2 , 𝑦2 is the point:
Example
Find the length, slope and midpoint of 𝐴𝐵 for A(-3, 4)
and B(5, 7).
The midpoint of a segment is (4, -6). If one endpoint is
(11, -16), what is the other endpoint?
Verify the Triangle Midsegment Theorem for a single
midsegment in Δ𝐴𝐵𝐶, given A(-5, 3), B(3, 5), and C(-1, -3).
Prove that the quadrilateral PQRS is a parallelogram by showing
that the diagonals bisect each other: P(-1, -2), Q(1, 4), R(9, 7),
S(7, 1).
13-5 Homework
p. 545: #1-17 odd, 16