Question

directions: given the vertices, determine the quadrilaterals most specific classification: parallelogram, rectangle, rhombus, or square. justify your answer using the distance formula. 1. s(-9, 14), t(1, 10), u(-3, 0), v(-13, 4) 2. e(-7, -4), f(2, -3), g(0, -7), h(-9, -8)

Explanation:

Step1: Calculate the lengths of the sides

The distance formula is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)
For \(EF\): \(x_1=-7,y_1 = - 4,x_2=2,y_2=-3\)
\(EF=\sqrt{(2 + 7)^2+(-3 + 4)^2}=\sqrt{81 + 1}=\sqrt{82}\)
For \(FG\): \(x_1=2,y_1=-3,x_2=0,y_2=-7\)
\(FG=\sqrt{(0 - 2)^2+(-7 + 3)^2}=\sqrt{4+16}=\sqrt{20}\)
For \(GH\): \(x_1=0,y_1=-7,x_2=-9,y_2=-8\)
\(GH=\sqrt{(-9 - 0)^2+(-8 + 7)^2}=\sqrt{81+1}=\sqrt{82}\)
For \(HE\): \(x_1=-9,y_1=-8,x_2=-7,y_2=-4\)
\(HE=\sqrt{(-7 + 9)^2+(-4 + 8)^2}=\sqrt{4 + 16}=\sqrt{20}\)

Step2: Analyze the properties of the quadrilateral

Since \(EF = GH=\sqrt{82}\) and \(FG=HE=\sqrt{20}\), the opposite sides are equal.

Answer:

Parallelogram