Question

find the point on x axis which is equidistant from the point (-2 5) and (2,9)​

Answer 1

$\underline{\textsf{Given:}}$

$\textsf{Points\;are\;(-2,5)\;and\;(2,9)}$

$\underline{\textsf{To find:}}$

$\textsf{The point on x axis which is equidistant from}$

$\textsf{the given two points}$

$\underline{\textsf{Solution:}}$

$\textsf{Let the given points be A(-2,5) and B(2,9)}$

$\textsf{Let the required point on x axis be P(h,0)}$

$\textsf{As per given data,}$

$\mathsf{PA=PB}$

$\mathsf{\sqrt{(h+2)^2+(0-5)^2}=\sqrt{(h-2)^2+(0-9)^2}}$

$\mathsf{\sqrt{(h+2)^2+25}=\sqrt{(h-2)^2+81}}$

$\mathsf{Squaring\;on\;bothsides\;we\;get}$

$\mathsf{h^2+4+4h+25=h^2+4-4h+81}$

$\mathsf{4h+25=-4h+81}$

$\mathsf{4h+4h=81-25}$

$\mathsf{8h=56}$

$\mathsf{h=\dfrac{56}{8}}$

$\implies\mathsf{h=7}$

$\underline{\textsf{Answer:}}$

$\textsf{The required point on x axis is (7,0)}$

$\underline{\textsf{Find more:}}$

Find the point on y-axis which is equidistant from the points (5,- 2) and (- 3,2)

https://brainly.in/question/8037323

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

https://brainly.in/question/21994280