Question

a rectangle has vertices at $(-2, 1)$, $(3, 1)$, $(3, -2)$, and $(-2, -2)$. what is the area of the rectangle? \\(\bigcirc\\) a. 8 square units \\(\bigcirc\\) b. 10 square units \\(\bigcirc\\) c. 12 square units \\(\bigcirc\\) d. 15 square units

Explanation:

Step1: Calculate length of base

The base is the distance between $(-2,1)$ and $(3,1)$. Since the y-values are equal, subtract x-values:
$3 - (-2) = 5$

Step2: Calculate length of height

The height is the distance between $(3,1)$ and $(3,-2)$. Since the x-values are equal, subtract y-values:
$1 - (-2) = 3$

Step3: Compute area of rectangle

Area is base multiplied by height:
$\text{Area} = 5 \times 3$

Answer:

D. 15 square units