(1) The locus of points equidistant from the lines `y=2x` and `y=-2x` .

Note that these two lines intersect at the origin.

**The locus of points equidistant fromthe two lines are the points on the line x=0 (the y-axis) and the points on the line y=0 (the x-axis).**

You can see this from the graphs.

Another way to realize this is to see that y=-2x is a reflection of the line y=2x about the x-axis [If g(x)=-2x and f(x)=2x then g(x)=-f(x)] and also a reflection over the y-axis [g(x)=f(-x)]

Note that the lines form vertical angles. The axes bisect the angles and from geometry we have a point on the angle bisector is equidistant from the sides of the angle.

**(2) The locus of points equidistant to the lines `y=2"and"y=8` is the line y=5**

Each point on y=5 is three units from y=2 and y=8.

## We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

- 30,000+ book summaries
- 20% study tools discount
- Ad-free content
- PDF downloads
- 300,000+ answers
- 5-star customer support

Already a member? Log in here.

Are you a teacher? Sign up now