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Given: W(-1,1), X(3,4), Y(6,0), and Z(2,3) are the vertices of quadrilateral WXYZ.

Prove: WXYZ is a square using the distance formula.

I found ________.

Answer :

All four sides, WX, XY, YZ, and ZW, have a length of 5 units each, we can conclude that all four sides have the same length. This indicates that quadrilateral WXYZ is indeed a square.

To determine if quadrilateral WXYZ is a square, we need to analyze the properties of a square. One key property of a square is that all four sides are of equal length.

Using the distance formula to calculate the distance between the vertices of the quadrilateral:

1. Distance between W(-1,1) and X(3,4):

WX = [tex]\sqrt{(3 - (-1))^2 + (4 - 1)^2} = \sqrt{16 + 9} = \sqrt{25} = 5[/tex]

2. Distance between X(3,4) and Y(6,0):

XY = [tex]\sqrt{(6 - 3)^2 + (0 - 4)^2} = \sqrt{9 + 16} = \sqrt{25} = 5[/tex]

3. Distance between Y(6,0) and Z(2,-3):

YZ = [tex]\sqrt{(2 - 6)^2 + (-3 - 0)^2} = \sqrt{16 + 9} = \sqrt{25} = 5[/tex]

4. Distance between Z(2,-3) and W(-1,1):

ZW = [tex]\sqrt{(-1 - 2)^2 + (1 - (-3))^2} = \sqrt{9 + 16} = \sqrt{25} = 5[/tex]

Since all four sides, WX, XY, YZ, and ZW, have a length of 5 units each, we can conclude that all four sides have the same length. This indicates that quadrilateral WXYZ is indeed a square.

Therefore, the correct answer is: option (c)all four sides have a length of 5

Question :

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Rewritten by : Barada

The quadrilateral WXYZ is not a square using the distance formula

Proving WXYZ is a square using the distance formula

From the question, we have the following parameters that can be used in our computation:

W(-1,1),X(3,4),Y(6,0) and Z(2,3)

The lengths of the sides can be calculated using the following distance formula

Length = √[Change in x² + Change in y²]

Using the above as a guide, we have the following:

WX = √[(-1 - 3)² + (1 - 4)²] = 5

XY = √[(3 - 6)² + (4 - 0)²] = 5

YZ = √[(6 - 2)² + (0 - 3)²] = 5

ZW = √[(2 + 1)² + (3 - 1)²] = 13

The sides that are congruent are WX, XY and YZ

This means that WXYZ is not a square

Read more about distance at

brainly.com/question/28551043

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