Question

Points $P(1,3)$ and $Q(-5,-5)$ are two points in the coordinate plane. The X-coordinate of the point equidistant from the points $P$ and $Q$ and lying on the line $y=-1$ is

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Answer 1

The required point is equidistant from the points $P$ and $Q$, and also lies on the line $y=-1$.

Let the point be $A$, it lies on $y=-1$

Therefore consider the point $A(x_a,-1)$

$DistanceAP=DistanceAQ$

$\sqrt{(x_a-1{)}^2+(-1-3{)}^2})$ = $\sqrt{(x_a+5{)}^2+(-1+5{)}^2}$
${(x_a-1)}^2$ + $(-4{)}^2$ = ${(x_a+5)}^2$ + $(4{)}^2$
$-2x_a+1=10x_a+25$
$-12x_a=24$
$x_a=-2$
The coordinates of the point $A$ is $(-2,-1)$.