Question

Show that the points P(-2, 6), Q (3, 1), R(-1, -3) and S(-6, 2) are the vertices
of a rectangle PQRS.
Solve in graph

Answer 1

P(-2,6), Q(3,1), R(-1,3), S(-6,2)

PQ = √(3 - (-2)² + (1 - (6))²

= √(5)² + (-5)²

= √25 + 25 = √50

QR = √(3 - (-1))² + (1 - 3)²

= √(4)² + (-2)²

= √16 + 4 = √20

RS = √((-1)-(-6))² + (3 -2)²

= √(5)² + (1)²

= √25 + 1 = √26

PS = √((-6)-(-2))² + (2-6)²

= √(-4)² + (-4)²

= √16 + 16 = √32

PR = √((-1)-(-2))² + (3-6)²

= √(1)² + (-3)²

= √1+9 = √10

QS = √(3 - (-6))² + (1 - 2)²

= √(9)² + (-1)²

= √81 + 1 = √82