Question

Quadrilateral ABCD has coordinates A (3, 5), B (5, 2), C (8, 4), D (6, 7). Quadrilateral ABCD is a

Answer 1

Square.
1. Gradients of AB and DC are equalits a parallelogram
2. Distances of AB and BC are equal＋its a parallelogramit's a square

Answer 2

The parallelogram ABCD is a square with side length of

`√(13)`.

Explanation:

The coordinates of the given quadrialteral ABCD are

`A(3,5)\\B(5,2)\\C(8,4)\\D(6,7)`

The best way to see which type of quadrilateral is, it's to draw.

The image attached shows the quadrilateral ABCD. According to our figure, it seems to be a square.

To demonstrate that the parallelogram ABCD is a square, we need to find the length of each side.

`AB=\sqrt{(2-5)^(2) +(5-3)^(2) } =√(9+4)=√(13)`

`BC=\sqrt{(4-2)^(2) +(8-5)^(2) } =√(4+9)=√(13)`

`CD=\sqrt{(7-4)^(2) +(6-8)^(2) } =√(9+4)=√(13)`

`DA=\sqrt{(7-5)^(2) +(6-3)^(2) } =√(4+9)=√(13)`

Therefore, the parallelogram ABCD is a square with side length of
`√(13)`.