Question

Find the point on x-axis which is equidistant from the points (−2, 5) and (2,−3).

Answer 1

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

Here we are to find out a point on the x-axis which is equidistant from both the points A(−2,5) and B(2,−3)

Let this point be denoted as C(x, y).

Since the point lies on the x-axis the value of its ordinate will be 0. Or in other words we have.

Now let us find out the distances from ‘A’ and ‘B’ to ‘C’

We know that both these distances are the same. So equating both these we get,

Squaring on both sides we have,

Hence the point on the x-axis which lies at equal distances from the mentioned points is.