The x-coordinate of a point P is twice its y-coordinate. If P is equidistant from Q(2,-5) and R(-3,6), find the coordinates of P.

Question

Philoid · Accepted Answer

From the condition given in the question the figure can be drawn as follows:

Let us assume the point P be (2k, k), Q (2, -5) and R (-3, 6)

It is given in the question that,

PQ = PR

Now, by squaring both sides we get:

PQ² = PR²

_{(2k, k)}² + (k + 5)² = (2k + 3)² + (k – 6)²

_{2k + 29 = 45}

_{2k = 16}

_{k = 8}

_{Hence, the coordinates of point P is (16, 8)}