   SEARCH HOME Math Central Quandaries & Queries  Question from abeth, a teacher: If (x, 4) is equidistant from (5, -2) and (3, 4), find x. Find the point on the y - axis that is equidistant from (-4, -2) and (3, 1). 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     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.