Question

The point on the x-axis which is equidistant from the points (6, -2) and (5, 4) is ​

Answer 1

$\textbf{Given:}$

$\text{Points are (6, -2) and (5, 4)}$

$\textbf{To find:}$

$\text{The point on x-axis which is equidistant from the given two points}$

$\textbf{Solution:}$

$\text{Let the given points be A(6, -2) and B(5, 4)}$

$\text{Let the required points on x axis be P(x,0)}$

$\text{As per given data,}$

$\bf\,AP=BP$

$\sqrt{(x-6)^2+(0+2)^2}=\sqrt{(x-5)^2+(0-4)^2}$

$\sqrt{(x-6)^2+4}=\sqrt{(x-5)^2+16}$

$\text{Squaring on bothsides, we get}$

$(x-6)^2+4=(x-5)^2+16$

$x^2+36-12x+4=x^2+25-10x+16$

$40-12x=41-10x$

$40-41=12x-10x$

$-1=2x$

$\implies\bf\,x=\dfrac{-1}{2}$

$\textbf{Answer:}$

$\textbf{The required point on x-axis is}$

$\bf(\dfrac{-1}{2},0)$