Question

The coordinates of the point on X-axis which are equidistant from the points (−3, 4) and (2, 5) are

Options

• (20, 0)

• (−23, 0)

• \[\left( \frac{4}{5}, 0 \right)\]

   

• None of these  

Answer 1

Let the point be A(a,0)  be equidistant from the two given points P (−3, 4) and Q (2, 5).

So applying distance formula, we get,

`AP^2 = AQ^2`

Therefore,

`(a + 3)^2 + (-4)^2 = (a - 2)^2 + 5^2`

                           10a = 4

                              ` a = 2/5`

Hence the co-ordinates of A are  `(2/5 , 0)`