Question

1. what is the area (in units²) of a rectangle in the (x,y)-coordinate plane that has vertices at (-4,3), (4,3), (4,0), and (-4,0)?

a) 12 units²
b) 16 units²
c) 24 units²
d) 64 units²

Explanation:

Step1: Find the length of the base

The difference in the x - coordinates of two points with the same y - coordinate gives the length of the base. Points (-4,3) and (4,3) have the same y - coordinate. The length of the base $b=\vert4 - (-4)\vert=8$.

Step2: Find the length of the height

The difference in the y - coordinates of two points with the same x - coordinate gives the height. Points (4,3) and (4,0) have the same x - coordinate. The height $h=\vert3 - 0\vert = 3$.

Step3: Calculate the area of the rectangle

The area of a rectangle is given by the formula $A = b\times h$. Substituting $b = 8$ and $h=3$, we get $A=8\times3 = 24$.

Answer:

C. 24 units²