Prove conjectures about geometric figures on a coordinate plane.

1. Obj. 19 Coordinate Proof
The student is able to (I can):
• Prove conjectures about geometric figures on a
coordinate plane

2. coordinate
proof
Example
A style of proof that uses coordinate
geometry and algebra. Once a figure is
placed in the coordinate plane, we can use
slope, the coordinates of the vertices, the
Distance Formula, or the Midpoint Formula
to prove statements about the figure.
Given: Rectangle ABCD with A(0, 0),
B(4, 0), C(4, 10), and D(0, 10)
Prove: The diagonals bisect each other.
The midpoint of AC is (2, 5), and the
midpoint of BD is also (2, 5). Therefore,
the two diagonals bisect each other.

3. Example
Given: A(0, 0), B(7, 1), C(10, 5), and D(3, 4)
Prove: ADB @ CBD
D
C
B
A
AB = (7 − 0)2 + (1− 0)2 = 50
( ) ( ) 2 2 AD = 3 − 0 + 4 − 0 = 5
( ) ( ) 2 2 CB = 10 − 7 + 5 − 1 = 5
( ) ( ) 2 2 CD = 3 − 10 + 4 − 5 = 50
Therefore, AD @ CB and AB @ CD
DB @ BD by Refl. prop. @
Therefore, ADB @ CBD by SSS