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Answer 1

The quadrilateral with vertices at the  points: (0,0), (3,2), (6,0), (3,-2) is a square

The vertices (or coordinates) of the quadrilateral is given as:

$(x,y) = (0,0), (3,2), (6,0), (3,-2)$

Calculate the distance between subsequent points, using the following distance formula

$d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2}$

So, we have:

$AB = \sqrt{(0 -3)^2 + (0 -2)^2}$

$AB = \sqrt{13}$

$BC = \sqrt{(3 -6)^2 + (2 -0)^2}$

$BC = \sqrt{13}$

$CD = \sqrt{(6 -3)^2 + (0 --2)^2}$

$CD = \sqrt{13}$

$DA = \sqrt{(3 -0)^2 + (-2 -0)^2}$

$DA = \sqrt{13}$

Notice that the sides of the quadrilateral are congruent.

Hence, the quadrilateral is a square

Read more about quadrilaterals at:

brainly.com/question/1543115