Question

What is the area of a parallelogram if the coordinates of its vertices are (0, -2), (3,2), (8,2), and (5, -2)?A. 20 units²B. 32 units²C. 10 units²D. 25 units²

Answer 1

Let's draw the parallelogram in the coordinate plane. This is shown below:

The area of a parallelogram is given by the formula

$A=bh$

Where

b is the length of base

h is the height

Let's draw the sides b, h on the diagram:

The length of the base, b, is "5 - 0 = 5 units".

The height, h, is the distance between the points (3,2) and (3, -2). We will use the distance formula to find the length (h).

Distance Formula

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

Where

Given,

$\begin{gathered} (x_1,y_1)=(3,2) \\ (x_2,y_2)=(3,-2) \end{gathered}$

So, the height is:

$\begin{gathered} d=\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2} \\ h=\sqrt[]{(-2-2)^2+(3-3)^2} \\ h=\sqrt[]{(-4)^2+0} \\ h=\sqrt[]{16} \\ h=4 \end{gathered}$

We now know, b = 5 units and h = 4 units

Thus, the area of the parallelogram is >>>>

$\begin{gathered} A=bh \\ A=5\times4 \\ A=20 \end{gathered}$Answer

A. 20 units²