Title: Example 1 Geometric Mean
Author: Tim Heppner
Last saved by: MHE
Company: MCGRAW-HILL

Geometry	Chapter 6

Lesson 6-7

Example 1  Positioning a Square
Position and label a square with sides n units long on the coordinate plane.
•	Let A, B, C, and D be vertices of the square.
•	Place A at the origin. As a result,  is on the 	
positive x-axis and  is on the y-axis. Label 
the vertices A, B, C, and D.
•	The y-coordinate of B is 0 because the vertex is 
on the x-axis. Since the side length is n, 
the x-coordinate is n.
•	D is on the y-axis so the x-coordinate is 0. 
The y-coordinate is 0 + n or n.
•	The x-coordinate of C is also n. The y-coordinate is 
0 + n or n because the side is n units long.

Example 2  Find Missing Coordinates
Name the missing coordinates for the parallelogram.	
Opposite sides of a parallelogram are congruent and parallel. 
So, the y-coordinate of C is b. 

The length of  is a, and the length of  is a. 
The x-coordinate of C is a units more than the x-coordinate of D.
So, the x coordinate of C is a + c.

The coordinates of C are (c + a, b).

Example 3  Coordinate Proof
Given:	Quadrilateral FHJK	
Prove:	FHJK is an isosceles trapezoid

Proof:
Use the Distance Formula to find the length of  and .

FK	= 
	=

HJ	= 
	=

Find the slopes of  and .

slope of 	= 
	=  or 0

slope of 	= 
	=  or 0

FHJK is an isosceles trapezoid because one set of opposite sides is parallel and the other set of opposite sides are congruent.

Example 4  Properties of Quadrilaterals
AIRPLANES  Write a coordinate proof to prove that	
the paths of the two airplanes will not cross.
Given:	A(0, 0), B(7, -4), C(-7, 0), D(0, -4)
Prove:	║

Proof:
slope of 	=  or -
slope of 	=  or -
Since  and  have the same slope, they are parallel.