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.
As given Q(0,1) is equidistant from P(5,−3) and R(x,6)
⇒PQ=QR
⇒√(0−5)2+(1−(−3))2=√(x−0)2+(1−6)2 [ By using disatnce formula =√(x2−x1)2+(y2−y1)2 ]
⇒25+16=x2+25
⇒41=x2+25
⇒x2=16
⇒x=4
Distance between Q(0,1) and R(4,6)
QR=√(4−0)2+(6−1)2=√42+52=√16+25=√41
Distance between P(5,−3) and R(4,6)
PR=√(4−5)2+(6+3)2=√1+81=√82