Question

If the points (2, 1) and (1, −2) are equidistant from the point (x, y), show that x + 3y = 0.

Answer 1

The distance d between two points and is given by the formula

Here it is said that the points (2, 1) and (1, −2) are equidistant from (x, y).

Let be the distance between (2, 1) and (x, y).

Let be the distance between (1, −2) and (x, y).

So, using the distance formula for both these pairs of points we have

Now since both these distances are given to be the same, let us equate both and

Squaring on both sides we have,

Hence we have proved that when the points (2, 1) and (1,−2) are equidistant from (x, y) we have .