Question

The co-ordinates of the point on x-axis which is equidistant from the points A(5, 4) and B(– 2, 3) is:

• A. (2,0)
• B. (3,0)
• C. (0,2)
• D. (0,3)

Answer 1

The correct option is A

(2,0)

Any point on x axis is of the form C(x, 0)

Given that AC = BC

$\Rightarrow A{C}^2$ = $B{C}^2$

$\Rightarrow {(x-5)}^2$ + $4^2$ = ${(x+2)}^2$+ $3^2$
$\Rightarrow x^2$ + 25 - 10x + 16 = $x^2$ + 4 + 4x + 9
$\Rightarrow 14x=28$
$\Rightarrow x=2$