Question

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

Answer 1

The distance d between two points (x₁,y₁) and (x₂,y₂) is given by the formula

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

Let this point be denoted as C(x, y).

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

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,

AC = BC

Hence the point on the y-axis which lies at equal distances from the mentioned points is (0, -2).