Question

What type of a quadrilateral do the points A(2, –2), B(7, 3), C(11, –1) and D(6, –6) taken in that order, form?

Answer 1

The points are A(2, –2), B(7, 3), C(11, –1) and D(6, –6)

Using distance formula,

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

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

= `sqrt((5)^2 + (5)^2`

= `sqrt(25 + 25)`

= `sqrt(50)`

= 5`sqrt(2)`

BC = `sqrt((11 - 7)^2 + (-1 - 3)^2`

= `sqrt((4)^2 + (-4)^2`

= `sqrt(16 + 16)`

= `sqrt(32)`

= `4sqrt(2)`

CD = `sqrt((6 - 11)^2 + (-6 + 1)^2`

= `sqrt((-5)^2 + (-5)^2`

= `sqrt(25 + 25)`

= `sqrt(50)`

= `5sqrt(2)`

DA = `sqrt((2 - 6)^2 + (-2 + 6)^2`

= `sqrt((-4)^2 + (4)^2`

= `sqrt(16 + 16)`

= `sqrt(32)`

= `4sqrt(2)`

Finding diagonals AC and BD, we get,

AC = `sqrt((11 - 2)^2 + (-1 + 2)^2`

= `sqrt((9)^2 + (1)^2`

= `sqrt(81 + 1)`

= `sqrt(82)`

And BD = `sqrt((6 - 7)^2 + (-6 - 3)^2`

= `sqrt((-1)^2 + (-9)^2`

= `sqrt(1 + 81)`

= `sqrt(82)`

The quadrilateral formed is rectangle.