Question

The point equidistant from P (1, 3) and Q (-5, -5) and lying on the line $y=-1$ is _____ .

• A. (1, 3)
• B. (-1, -4)
• C. (-3, 1)
• D. (-2, -1)

Answer 1

The correct option is D (-2, -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. Since it lies on $y=-1$, its y coordinate will be -1. Thus, the coordinates of point A will be (x, -1).

Distance AP = Distance AQ

$\Rightarrow {AP}^2={AQ}^2$

$\Rightarrow (x-1{)}^2+(-1-3{)}^2=(x-(-5){)}^2+(-1-(-5){)}^2\Rightarrow (x-1{)}^2+16=(x+5{)}^2+16\Rightarrow x^2-2x+1+16=x^2+10x+25+16\Rightarrow -2x+17=10x+41\Rightarrow -12x=24\Rightarrow x=-2$

Thus, the coordinates of point A will be (-2, -1).