Question

The coordinates of a quadrilateral are (1,3), (7,-3), (1,-9), and (-5,-3). What shape is formed? Select all that apply. -Kite -Rectangle -Rhombus -Square -Trapezoid

Answer 1

Answer: Sqaure

Explanation:

We obtain the figure by either plotting or finding the distances between the points:

`\begin{aligned}&\text { Distance } b / w \quad A B =\sqrt{(1-7)^(2)+(3-(-3))^(2)}\\&=\sqrt{6^(2)+6^(2)}\\&A B=√(72) \text { units }\end{aligned}`

`\text { Distance } b / w \quad BC =\sqrt{(7-1)^(2)+(-3-(-9))^(2)} \\BC=√(72) \text { units }`

`\begin{aligned}\text { Distance } b / w \ C D &=\sqrt{(1-(-5))^(2)+(-9-(-3))^(2)} \\C D=√(72) \text { units }\end{aligned}`

`$$ Distance $b/w \ A D=\sqrt{(1-(-5))^(2)+(3(-3))^(2)}$A D=√(72) \text { units }`

Since all the distances of the four sides are equal, we have to check if the shape is either a rhombus or a square by the measuring the length of the diagonals

`\begin{aligned}A C &=\sqrt{(1-1)^(2)+(3-(-9))^(2)} \\&=\sqrt{12^(2)} \\A C &=12 \text { units } \\B D &=\sqrt{(7-(-5))^(2)+(-3-(-3))^(2)} \\&=\sqrt{12^(2)} \\A C &=12 \text { units }\end{aligned}`

The diagonals are also equal; therefore, the figure is a square