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Question

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

A
(-2 , -1)
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B
(-4 , -1)
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C
(-3 , -1)
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Solution

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

(x1)2+(13)2=(x(5))2+(1(5))2(x1)2+16=(x+5)2+16x22x+1+16=x2+10x+25+162x+17=10x+4112x=24x=2

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

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