Question

5) Find the area of a rectangle
with points at (-8,5), (2,5),
(2,-3) and (-8,-3).

Answer 1

80 units

Explanation:

So first i plotted all of the points. Then i connected all the dots until i made a rectangle. Then I counted what the length and height of the rectangle is. Since the length x height = the area, then i multiplied the measurements together. Then i got 80 units. Here is a picture below (sorry for the bad quality its night where i live)

Answer 2

80 units²

Explanation:

Given vertices of a rectangle:

• A = (-8, 5)
• B = (2, 5)
• C = (2, -3)
• D = (-8, -3)

As points A and D share the same x-coordinate, and points B and C share the same x-coordinate, the difference between the different x-coordinates is the length of the rectangle:

`\begin{aligned}\implies \textsf{Length} & = x_B-x_A\\& = 2-(-8)\\& = 2+8\\& = 10\; \sf units\end{aligned}`

As points A and B share the same y-coordinate, and points C and D share the same y-coordinate, the difference between the different y-coordinates is the width of the rectangle:

`\begin{aligned}\implies \textsf{Width} & = y_A-y_D\\& = 5-(-3)\\& = 5+3\\& = 8\; \sf units\end{aligned}`

Therefore:

`\begin{aligned}\textsf{Area of a rectangle} & = \sf width * length\\&=8 * 10\\&=80 \sf \; units^2\end{aligned}`