CK-12 Geometry - Second Edition

3.6. The Distance Formula http://www.ck12.org

y=mx+b

5 = 1 ( 2 )+b

5 = 2 +b

3 =b

The equation of the perpendicular bisector isy=x+3.

Example 7:The perpendicular bisector ofABhas the equationy=−^13 x+1. IfAis (-1, 8) what are the coordinates
ofB?

Solution:The easiest way to approach this problem is to graph it. Graph the perpendicular line and plot the point.
See the graph to the left.

Second, determine the slope ofAB. If the slope of the perpendicular bisector is−^13 , then the slope ofABis 3.

Using the slope, countdown3 and over to theright1 until you hit the perpendicular bisector. Counting down 6 and
over 2, you land on the line at (-3, 2). This is themidpointofAB. If you count down another 6 and over to the right
2 more, you will find the coordinates ofB, which are (-5, -4).