Author: Kathy Halverson
Last saved by: Glencoe Mathematics
Company: Halverson Household

Lesson 9-5

Example 1	Use the Distance Formula
Find the distance between M(1, 5) and N(-3, 2).  Round to the nearest tenth, if necessary.

Use the Distance Formula.
	d = 			Distance Formula
 MN = 			(x_1, y_1) = (1, 5), (x_2, y_2) = (-3, 2)
 MN = 				Simplify.
MN = 					Evaluate (-4)^2 and (-3)^2.
MN = 					Add 9 and 16.
MN = 5						Take the square root.
The distance between points M and N is 5 units.

Example 2	Use the Distance Formula to Solve a Problem
GEOMETRY	Find the perimeter of ΔABC to the nearest tenth.

First, use the Distance Formula to find the length of each side of the triangle.

Side : A(-1, 5), B(4, 0)
      d	 = 			
   AB 	= 
   AB 	= 
   AB 	= 	
   AB 	= 				                                             
                                                                 
 Side : B(4, 0), C(-2, -3)			Side : C(-2, -3), A(-1, 5)
      d =                                d	= 
   BC	=                              CA 	= 
   BC =                                         CA	=      
   BC =                                                    CA 	= 
   BC =                                                          CA 	= 	
           		
Then add the lengths of the sides to find the perimeter.
 +  +  ≈ 7.071 + 6.708 + 8.062
			    ≈ 21.841
The perimeter is about 21.8 units.

Example 3	Use the Distance Formula to Solve a Problem
INVESTIGATION     A detective creates a coordinate system to record where pieces of evidence were located.  A unit on the grid represents 2 feet.  Find the distance between two pieces of evidence if one was found at (-4, 3) and the other was found at (5, -2) on the grid.  Round to the nearest tenth, if necessary.

Let d = the distance between the two pieces of evidence.  Use the distance formula.
   d	= 	Distance Formula
   d	=   	(x_1, y_1) = (-4, 3), (x_2, y_2) = (5, -2)
   d = 		Add.
   d = 			Simplify.
   d = ≈ 10.3			Take the square root.

The distance between the two pieces of evidence is 10.3 units of the grid.  Since each unit equals 2 feet, the distance between the two pieces of evidence is 2 × 10.3 or 20.6 feet.