Question

Name the type of quadrilateral formed, if any, by the following point, and give reasons for your answer:

 (−3, 5), (3, 1), (0, 3), (−1, −4)

Answer 1

Let the points (−3, 5), (3, 1), (0, 3), and (−1, −4) be representing the vertices A, B, C, and D of the given quadrilateral respectively.

AB = `sqrt((-3,-3)^2 + (5-1)^2)`

= `sqrt((-6)^2+(4)^2)`

= `sqrt(36+16)`

= `sqrt(52)`

= `2sqrt13`

BC = `sqrt((3-0)^2+(1-3)^2)`

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

= `sqrt(9+4)`

= `sqrt13`

CD = `sqrt((0-(-1))^2+(3-(-4))^2)`

= `sqrt((1)^2+(7)^2)`

= `sqrt(1+49)`

= `sqrt50`

= `5sqrt2`

AD = `sqrt((-3-(-1))^2+(5-(-4))^2)`

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

= `sqrt(4+81)`

= `sqrt85`

AC = `sqrt ([0 - (-3)^2] + (3 - 5)^2)`

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

= `sqrt (9 + 4)`

= `sqrt13`

BD = `sqrt ((-1 - 3)^2 + (-4 - 1)^1)`

= `sqrt ((-4)^2 + (5)^2)`

= `sqrt (16 + 25)`

= `sqrt41`

It can be observed that all sides of this quadrilateral are of different lengths. Therefore, it can be said that it is only a general quadrilateral, and not specific such as square, rectangle, etc.