Question

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

A(−3, 1), B(−6, −7), C(3, −9) and D(6, −1)

Answer 1

Distance = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`

AB = `sqrt((-6 + 3)^2 + (-7 - 1)^2`

= `sqrt((- 3)^2 + (- 8)^2`

= `sqrt(9 + 64)`

= `sqrt(73)`

BC = `sqrt((3 + 6)^2 + (-9 + 7)^2`

= `sqrt(9^2 + (-2)^2`

= `sqrt(81 + 4)`

= `sqrt(85)`

CD = `sqrt((6 - 3)^2 + (-1 + 9)^2`

= `sqrt((3)^2 + (8)^2`

= `sqrt(9 + 64)`

= `sqrt(73)`

AD = `sqrt((6 + 3)^2 + (-1 - 1)^2`

= `sqrt((9)^2 + (-2)^2`

= `sqrt(81 + 4)`

= `sqrt(85)`

AB = CD = `sqrt(73)` and BC = AD = `sqrt(85)` ...(Opposite sides are equal)

∴ ABCD is a parallelogram.