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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

=(23)2+(48)2=(2+10)2+(4y)2

[ Distance between the points (x1,y1) and (x2,y2),d=(x2x1)2+(y2y1)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+160145=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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