The correct option is A (-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
⇒AP2=AQ2
⇒(x−1)2+(−1−3)2=(x−(−5))2+(−1−(−5))2⇒(x−1)2+16=(x+5)2+16⇒x2−2x+1+16=x2+10x+25+16⇒−2x+17=10x+41⇒−12x=24⇒x=−2
Thus, the coordinates of point A will be (-2,-1).