Question

Name the quadrilateral formed, if any, by the following points, and given reasons for your answers:

A(-3, 5) B(3, 1), C (0, 3), D(-1, -4)

Answer 1

A (-3,5) , B(3,1), C(0,3), D(-1,-4)

Let A, B, C and D be the four vertices of the quadrilateral ABCD.

We know the distance between two points `P(x_1, y_1)` and `Q(x_2, y_2)` is given by distance formula:

`PQ = sqrt((x_2 - x_1)^2 + (y_2 - y^1)^2)`

Hence

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

`=> AB = sqrt((6)^2 + (4)^2)`

`=> AB = sqrt(36 + 16)`

`=> AB= sqrt52`

`=> AB = 2sqrt13`

Similarly,

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

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

`=> BC = sqrt(9 + 4)`

`=> BC = sqrt(13)`

Similarly,

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

`=> CD = sqrt((-1)^2 + (-7)^2)`

`=> CD = sqrt(1 + 49)`

`=> CD = sqrt50` 

`=>CD = 5sqrt2`

Also

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

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

`=> DA = sqrt85`

Hence from the above we see that it is not a quadrilateral.