# Graph Problem

• Sep 17th 2011, 01:06 PM
PseudoThesis
Graph Problem
I'm having trouble determining what format my answer is supposed to take in the following problem:

The point P(x,y) satisfies the condition that is equidistant from the points A(4,1) and B (-3,5). Find and simplify an equation relating x and y. By simplify, we mean that you should re-write your equation so there are no square roots or fractional exponents present.

I know that one possible location for P is (0.5,3), which is also the midpoint of AB. They apparently want me to create an equation that equals zero. I tried y-6x, but was told that is incorrect.

What do they mean by "an equation relating x and y"?
• Sep 17th 2011, 01:11 PM
Plato
Re: Graph Problem
Quote:

Originally Posted by PseudoThesis
I'm having trouble determining what format my answer is supposed to take in the following problem:

The point P(x,y) satisfies the condition that is equidistant from the points A(4,1) and B (-3,5). Find and simplify an equation relating x and y. By simplify, we mean that you should re-write your equation so there are no square roots or fractional exponents present.

Write the equation of the line perpendicular to the line segment at the midpoint.
• Sep 17th 2011, 01:48 PM
PseudoThesis
Re: Graph Problem
I'm sorry, but I don't understand how to do that. Wouldn't a perpendicular line fall on C(-4,1) and D(3,5)? If so, how do I write an equation for this?
• Sep 17th 2011, 01:53 PM
Plato
Re: Graph Problem
Quote:

Originally Posted by PseudoThesis
I'm sorry, but I don't understand how to do that. Wouldn't a perpendicular line fall on C(-4,1) and D(3,5)? If so, how do I write an equation for this?

You know the midpoint $(-0.5,3)$.
The slope of $\overleftrightarrow {CD}$ is $\frac{4}{7}$.
So the slope of the perpendicular is $\frac{-7}{4}$.
Write the equation.