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Question

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

Solution
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As given Q(0,1) is equidistant from P(5,3) and R(x,6)


PQ=QR
(05)2+(1(3))2=(x0)2+(16)2 [ By using disatnce formula =(x2x1)2+(y2y1)2 ]

25+16=x2+25

41=x2+25

x2=16

x=4

Distance between Q(0,1) and R(4,6)

QR=(40)2+(61)2=42+52=16+25=41

Distance between P(5,3) and R(4,6)

PR=(45)2+(6+3)2=1+81=82

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