Find a point on the x-axis which is equidistant from the points (… - Vidyadip

Question

Find a point on the $x-$axis which is equidistant from the points $(7, 6)$ and $(-3, 4).$

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Answer

Let $A(7, 6)$ and $B(-3, 4)$ be the given points.
Let $P(x, 0)$ be the point on $x-$axis such that $PA = PB$
$ P A=P B $
$ P A^2=P B^2 $
$ (x-7)^2+(0-6)^2=(x+3)^2+(0-4)^2 $
$ \Rightarrow x^2+49-14 x+36=x^2+9+6 x+16 $
$ \Rightarrow x^2-14 x-x^2-6 x=9+16-36-49 $
$ \Rightarrow-20 x=-60 $
$ \Rightarrow x=3$
$\therefore$ The point on $x-$axis is $(3, 0).$

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