Question

using the figure below, find the area of the rectangle on the coordinate plane. what is the area of the rectangle in this figure? round to the tenths place. multiple - choice question 23.9 units² 20 units² 24 units² 24.4 units² rewatch

Explanation:

Step1: Find length of one - side

Use distance formula $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. For two adjacent vertices, say $(0,0)$ and $(3,3)$, $d_1=\sqrt{(3 - 0)^2+(3 - 0)^2}=\sqrt{9 + 9}=\sqrt{18}\approx4.2$.

Step2: Find length of adjacent side

For vertices $(0,0)$ and $(- 4,-4)$, $d_2=\sqrt{(-4 - 0)^2+(-4 - 0)^2}=\sqrt{16 + 16}=\sqrt{32}\approx5.7$.

Step3: Calculate area

Area of rectangle $A = d_1\times d_2$. $A=\sqrt{18}\times\sqrt{32}=\sqrt{18\times32}=\sqrt{576}=24$.

Answer:

24 square units