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Question

# If the point A(2,-4) is equidistant from P(3,8) and Q(-10,y), then find the value of y.

A

-3

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B

4

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C

5

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D

-5

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Solution

## The correct options are A -3 D -5 According to the question, A(2,-4) is equidistant from P(3,8) amd Q(-10,y). i.e.,PA = QA ⇒=√(2−3)2+(−4−8)2=√(2+10)2+(−4−y)2 [∵ Distance between the points (x1,y1) and (x2,y2),d=√(x2−x1)2+(y2−y1)2] ⇒√(−1)2+(−12)2=√(12)2+(4+y)2 ⇒√1+144=√144+16+y2+8y ⇒√145=√160+y2+8y On squaring both the sides, we get 145=160+y2+8y ⇒y2+8y+160−145=0 ⇒y2+8y+15=0 ⇒y2+5y+3y+15=0 ⇒y(y+5)+3(y+5)=0 ⇒(y+5)(y+3)=0 If y+5=0, then y=−5 If y+3=0, then y=−3 ∴y=−3 and −5 Hence, the values of y are -3, -5.

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