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Question

If Q(0,1) is equidistant from P(5,3) and R(x,6) find the values of x.

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Solution

Q(0,1) is equidistant from P(5,3) and R(x,6).
So PQ=QR
By distance formula, [(50)2+(31))2]=[(x0)2+(61)2
[(5)2+(42]=[(x2+(5)2]
[(25+16)]=[x2+25]
(41)=[x2+25]
Squaring both sides,
41=x2+25
x2+2541=0
x216=0
(x4)(x+4)=0
(x4)=0 or (x+4)=0
x=4 or x=4
Hence the value of x is 4 or 4.

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