Question

the point on the x-axis equidistant from the point (-4,-3) and (-5,4) is​

Answer 1

$\underline{\textbf{Given:}}$

$\textsf{Poins are (-4,3) and (-5,4)}$

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

$\textsf{The point on x-axis equidistant from the given points}$

$\underline{\textbf{Solution:}}$

$\textsf{Let the given poins be A(-4,3) and B(-5,4)}$

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

$\textsf{As per the given data, PA=PB}$

$\implies\mathsf{\sqrt{(x+4)^2+(0-3)^2}=\sqrt{(x+5)^2+(0-4)^2}}$

$\implies\mathsf{\sqrt{(x+4)^2+9}=\sqrt{(x+5)^2+16}}$

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

$\implies\mathsf{(x+4)^2+9=(x+5)^2+16}$

$\implies\mathsf{x^2+16+8x+9=x^2+25+10x+16}$

$\implies\mathsf{8x+25=10x+41}$

$\implies\mathsf{8x-10x=41-25}$

$\implies\mathsf{-2x=16}$

$\implies\mathsf{x=-8}$

$\therefore\textbf{The required point on x-axis is (-8,0)}$

Answer 2

Step-by-step explanation:

Hope you get the correct answer.