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 PQ.

• A. PQ=QR=$\sqrt{41}$
• B. PQ=20, QR=$\sqrt{29}$
• C. PQ= $\sqrt{29}$, QR= 20
• D. PQ$=\sqrt{19}$, QR = 21

Answer 1

Answer: (A)

PQ=QR=$\sqrt{41}$

Q is equidistant from P and R

=>PQ=RQ

=>$P{Q}^2=R{Q}^2$

=>$(5{)}^2+(-4{)}^2=x^2+{\left(5\right)}^2=>x^2=16=>x=\pm 4$

Now PQ=QR=$\sqrt{16+25}=\sqrt{41}$