Abeth,

Let's try a slightly different question

If (x, -3) is equidistant from (-2, 1) and (3, 3), find x.

I would use the distance formula which says that if (a, b) and (c, d) are points in the plane then the distance between them is

√[(c - a)² + (d - b)²]

If the distance between (x, -3) and (-2, 1) is equal to the distance between (x, -3) and (3, 3) then

√[(1 - (-3))² + (-2 - x)²] = √[(3 - (-3))² + (3 - x)²]
=√[4² + (-2 - x)²] = √[6² + (3 - x)²].

Since the quantities under the root signs on both sides are positive

[4² + (-2 - x)²] = [6² + (3 - x)²].

Expanding I get

16 + 4 + 4x + x² = 36 + 9 - 6x + x²

thus

10x = 25 and hence x = 5/2.

You can now check by finding the distance between (5/2, -3) and (-2, 1), and the distance between (5/2, -3) and (3, 3)

Now you try your first problem. For the second problem, what do you know about the coordinates of a point on the y-axis?

Penny