Question

a rectangle is drawn on a coordinate plane with vertices (0,0), (2,2), (9, -4), and (7, -6). using the coordinates, what is the approximate area of the rectangle? (1 point) 26.08 units² 24.1 units² 52.2 units² 12.05 units²

Explanation:

Step1: Calculate the length of one side

Use the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). For points \((0,0)\) and \((2,2)\):
\(d_1=\sqrt{(2 - 0)^2+(2 - 0)^2}=\sqrt{4 + 4}=\sqrt{8}\approx2.83\)

Step2: Calculate the length of an adjacent side

For points \((2,2)\) and \((9,-4)\):
\(d_2=\sqrt{(9 - 2)^2+(-4 - 2)^2}=\sqrt{49+36}=\sqrt{85}\approx9.22\)

Step3: Calculate the area of the rectangle

The area of a rectangle \(A = l\times w\). Here \(l\approx9.22\) and \(w\approx2.83\)
\(A\approx9.22\times2.83 = 26.0926\approx26.08\)

Answer:

26.08 units²