Respuesta :

clarch19

Answer:

square

Step-by-step explanation:

all sides have the same length [tex]\sqrt{29}[/tex]

all vertices form 90 degree angles

The shape formed by vertices (-3,1), (2,3), (4,-2), (-1,-4) is Square.

Properties of Square:

  • A square is a quadrilateral with four equal sides and four equal angles each being 90° .
  • The diagonals of a square are equal and they bisect each other at 90°.

How to find if the shape of the given vertices is square?

There are 2 steps to find the shape of the vertices is square or not:

  • Find the distance between two vertices using distance formula. i.e.

                  [tex]d = \sqrt{(x_1 - x_2)^2 \ + \ (y_1 - y_2)^2[/tex]

So the length of the side of given vertices,

[tex]AB = \sqrt{(-3-2)^2 + (1-3)^2} = \sqrt{(25 + 4)} = \sqrt{29[/tex]

Similarly, BC = CD = DA = AB = [tex]\sqrt{29}[/tex]

  • If the Length of each side is equal it may be square. So the next check is for the length of the diagonal.

[tex]AC = \sqrt{(-3-4)^2 + (1-(-2))^2} = \sqrt{(49 + 9)} = \sqrt{58[/tex]

Similarly, BD = AC = [tex]\sqrt{58\\}[/tex]

Therefore, as all the sides and diagonals are equal, hence it is a square.

Learn more about the distance formula at:

https://brainly.com/question/19759821

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