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 distance 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