In this section, we will learn how to create an equation that represents the right bisector. A right bisector is a line that passes through the midpoint of a line at 90 degrees; it is sometimes called a perpendicular bisector. Given that it is a line, all lines can be represented in form:
y = mx + b
Where m represents the slope, and b represents the y-coordinate of the y-intercept.
Since the right bisector is at 90 degrees, in other words perpendicular to the line, you may need to touch up on a subject that you look at in Grade 9. Any line that is perpendicular to another has a slope that is the negative reciprocal of the other. So, if you have a slope m=3/2, the negative reciprocal of 3/2 is –2/3. This is explained in the video below.
- If you already familiar with this, you can skip to the next video.
Let’s take a look at an example involving the right bisector.
Two schools are located at the points P(-1,4) and Q(7,-2) on a town map. The school board is planning a new sports complex to be used by both schools. The board wants to find a location that is equidistant from the two schools. Use an equation to represent the possible locations for the sports complex.