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.

Answer 1

PQ = QR

√(5−0)2+(−3−1)2=√(0−x)2+(1−6)2
√(−5)2+(−4)2=√(−x)2+(−5)2
√25+16=√x2+25
41=x2+25
16=x2
x=±4

Therefore, point R is (4, 6) or ( - 4, 6).

When point R is (4, 6),

PR=√(5−4)2+(−3−6)2=√12+(−9)2
=√1+81=√82
QR=√(0−4)2+(1−6)2=√(−4)2+(−5)2
=√16+25=√41
When point R is (-4,6),
PR=√(5−(−4))2+(−3−6)2=√(9)2+(−9)2
=√81+81=9√2
QR=√(0−(−4))2+(1−6)2=√(4)2+(−5)2
=√16+25=√41