Title: Algebra 1
Author: Mandy McDaniel
Last saved by: Glencoe Mathematics

Lesson 10-5

Example 1 Distance Between Two Points
Find the distance between the points at (-1, 5) and (8, -7).
d = 	Distance Formula
	= 	(x, y) = (-1, 5) and (x, y) = (8, -7)
	= 	Simplify.
	= 	Evaluate squares and simplify.
	= 15 units

Example 2 Use the Distance Formula to Solve a Problem
Hai walks 5 blocks north then 7 blocks east to get from his home to work. To get from his home to school, he walks 3 blocks south then 2 blocks west. If he were able to walk the shortest possible distance from school to work, how far would he walk?	
Model the situation.
If his home is at (0, 0), then the location of his work
is (7, 5). The location of his school is (-2, -3). Use
the Distance Formula.
d = 	Distance Formula
	= 	(x, y) = (-2, -3), (x, y) = (7, 5)
	= 	Simplify.
	=  or about 12 blocks

Example 3 Find a Missing Coordinate
Find the value of r if the distance between the points at (-6, r) and (-2, 3) is 2.
	 d = 	Distance Formula
	2= 	Let x = -2, x = -6, y = 3, y = r, and d = 2 
	2= 
	2= 	Evaluate squares.
	2= 	Simplify.
	(2)= ()	Square each side.
	20 = r - 6r + 25	Simplify.
	0 = r - 6r + 5	Subtract 20 from each side.
	0 = (r – 1)(r – 5)	Factor.
	r – 1 = 0    or    r – 5 = 0	Zero Product Property
	r = 1	r = 5	The value of r is 1 or 5.