Question

Point on the $x$-axis which is equidistant from $(2,-5)$ and $(-2,9)$ is:

• A. $(-7,0)$
• B. $(14,0)$
• C. $(-14.0)$
• D. $(7,0)$

Answer 1

Answer: (A)

Given points $A(2,-5)$ and $B(-2,9)$
Let the points be $P(x,0)$.
So, $AP=PB$ and $A{P}^2=P{B}^2$
$\Rightarrow {(x-2)}^2+{(0+5)}^2={(x+2)}^2+{(0-9)}^2$
$\Rightarrow x^2+4-4x+25=x^2+4+4x+81$
$\Rightarrow x^2+29-4x=x^2+85+4x$
$\Rightarrow -4x-4x=85-29$
$\Rightarrow -8x=56$

$\Rightarrow x=-7$
Hence, point on the $x$-axis which is equidistant from $(2,-5)$ and $(-2,9)$ is $(-7,0)$.