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

Answer:

The parallelogram ABCD is a square with side length of

$\sqrt{13}$.

Step-by-step 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.

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

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

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

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

Therefore, the parallelogram ABCD is a square with side length of $\sqrt{13}$.