Question

Find a point on - axis which is equidistant from the points A (7,6) and B(-3,4).

Answer 1

Heya   

It seems you missed a point.
Correction :- Find a point on x - axis which is equidistant from the points A (7,6) and B(-3,4).
Your answer is here....

Let the points be A (7,6) and B (-3, 4). 
Let the third point be C.

It is given that the third point is on x axis. So, C (k, 0)   {Becoz. On x-axis, y=0 and we take k as x- coordinate).

Now, ATQ.
AC = BC.

So,
AC² = BC².

=> (7-k)² + (6-0)²    = (k+3)² + (0-4)²
=> 49 + k² - 14k + 36 = k² + 9 + 6k + 16 
=> 49 + 36 - 9 - 16 = 6k + 14k
=> 20k = 60
Hence, k = 3.

So, the coordinate C is C (3, 0) which is equidistant from A and B.

Hope it helps ...........