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

PQ = QR

[(5 - 0)² + (-3- 1)²]^1/2= [(0 - x)² + (1- 6)²]^1/2

41 = x² + 25

x² = 16

x =+-4

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

When point R is (4, 6)

PR = [(5 - 4)² + (-3 - 6)²]^1/2

QR = [(0 - 4)² + (1 - 6)²]^1/2

When point R is (- 4, 6),

PR = [(5 + 4)² + (-3 - 6)²]^1/2

QR = [(0+ 4)² + (1 - 6)²]^1/2