Question

Show that the following points taken in order to form the vertices of a parallelogram

A(−7, −3), B(5, 10), C(15, 8) and D(3, −5)

Answer 1

AB = `sqrt((5 + 7)^2 + (10 + 3)^2`

= `sqrt((12)^2 + (13)^2`

= `sqrt(144 + 169)`

= `sqrt(313)`

BC = `sqrt((15 - 5)^2 + (8 - 10)^2`

= `sqrt(10^2 + (-2)^2`

= `sqrt(100 + 4)`

= `sqrt(104)`

CD = `sqrt((3 - 15)^2 + (-5 - 8)^2`

= `sqrt((-12)^2 + (- 13)^2`

= `sqrt(144 + 169)`

= `sqrt(313)`

AD = `sqrt((3 + 7)^2 + (-5 + 3)^2`

= `sqrt((10)^2 + (-2)^2`

= `sqrt(100 + 4)`

= `sqrt(104)`

AB = CD = `sqrt(313)` and BC = AD = `sqrt(104)`  ...(Opposite sides are equal)

∴ ABCD is a parallelogram.