Question

Prove that the points (a, b), (a + 3, b + 4), (a − 1, b + 7) and (a − 4, b + 3) are the vertices of a parallelogram. 

Answer 1

PQ = `sqrt (("a" + 3 - "a")^2 + ("b" + 4 - "b")^2) = sqrt (9 + 16) = 5` units

QR = `sqrt (("a" + 3 - "a" + 1)^2 + ("b" - 4 - "b" - 7)^2) = sqrt (16 + 9) = 5` units

RS = `sqrt (("a" -1  - "a" + 4)^2 + ("b" + 7 - "b" - 3)^2) = sqrt (9 + 16) = 5` units

SP = `sqrt (("a" - 4 - "a")^2 + ("b" + 3 - "b")^2) = sqrt (16 + 9) = 5` units

Since the opposite sides of quadrilateral PQRS are equal, therefore it is a parallelogram.