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Select the correct answer from each drop-down menu.Glven: W(-1, 1), X(3, 4), Y(6, 0), and Z(2, -3) are the vertices of quadrilateral WXYZ.Prove: WXYZis a square.

Select the correct answer from each dropdown menuGlven W1 1 X3 4 Y6 0 and Z2 3 are the vertices of quadrilateral WXYZProve WXYZis a square class=

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ANSWER

all four sides have a length of 5

EXPLANATION

The distance between two points (x₁, y₁) and (x₂, y₂) is,

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

Let's find the distance between each pair of points, WX, XY, YX, and WZ,

[tex]WX=\sqrt{(3-(-1))^2+(4-1)^2}=\sqrt{(3+1)^2+(4-1)^2}=\sqrt{4^2+3^2}=\sqrt{16+9}=\sqrt{25}=5[/tex][tex]XY=\sqrt{(6-3)^2+(0-4)^2}=\sqrt{(3)^2+(-4)^2}=\sqrt{3^2+4^2}=\sqrt{9+16}=\sqrt{25}=5[/tex][tex]YZ=\sqrt{(2-6)^2+(-3-0)^2}=\sqrt{(-4)^2+(-3)^2}=\sqrt{4^2+3^2}=\sqrt{16+9}=\sqrt{25}=5[/tex][tex]WZ=\sqrt{(2-(-1))^2+(-3-1)^2}=\sqrt{(2+1)^2+(-4)^2}=\sqrt{3^2+4^2}=\sqrt{9+16}=\sqrt{25}=5[/tex]

Hence, using the distance formula we found that all four sides have a length of 5.