Question

The graph shows the location of point P and point R. Point R is on the y-axis and has the same y-coordinate as point P. Point Q is graphed at (n,-2). The distance from point P to point Q is equal to the distance from point P to point R. What is the from point P to point Q? What is the value of N? Explain how you determined the distance from point P to point Q, and the value of N.

Answer 1

The value of n such that the conditions are met is:

$n = \frac{2x \pm \sqrt{(-2x) - 4*1*(y + 2)^2} }{2}$

Where x and y are the coordinates of point P.

How to get the given points?

We know that:

• Q = (n, -2)
• R = (0, y)   (because R is on the y-axis).
• P = (x, y)

Now, the distance of P to Q is equal than the distance of P to R, then we have that:

$\sqrt{(x - 0)^2 + (y - y)^2} = \sqrt{(x - n)^2 + (y + 2)^2} \\\\x^2 = (x - n)^2 + (y + 2)^2$

So we need to solve this for n.

$x^2 = x^2 - 2xn + n^2 + y^2 + 4y + 4\\\\0 = -2xn +n^2 + (y + 2)^2\\\\\\0 = n^2 - (2x)*n + (y + 2)^2$

Notice that this is a quadratic of n, the two solutions of n will be:

$n = \frac{2x \pm \sqrt{(-2x) - 4*1*(y + 2)^2} }{2}$

Such that, as you can see, the value of n depends on x and y.

If you want to learn more about quadratic equations, you can read:

https://brainly.com/question/1214333