Question

Points P and Q 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 segment 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(xa,-1)

Distance AP = Distance AQ

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