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Question

A coordinate plane shows the x-axis ranging from negative 9 to 9 in unit increments and the y-axis ranging from negative 11 to 11 in unit increments. Four plotted points upper A upper B upper C upper D are joined to form a rectangle. The coordinates of the plotted points are as follows: point upper A is left parenthesis 3 comma 4 right parenthesis, point upper B is left parenthesis negative 5 comma 4 right parenthesis, point upper C is left parenthesis negative 5 comma 8 right parenthesis, and point upper D is left parenthesis 3 comma 8 right parenthesis.

Find the area of rectangle ABCD
in square feet.

(1 point)
Responses

−32
square feet
negative 32 square feet

32 square feet
32 square feet

24 feet
24 feet

32 feet

Answer 1

To find the area of rectangle ABCD, we first need to determine the lengths of its sides.

We can calculate the length of the rectangle by finding the distance between points A and B (on the same horizontal line) and points A and C (on the same vertical line).

1. Length of AB (horizontal side):

   • Point A: (3, 4)
   • Point B: (-5, 4)

   The length of side AB is calculated by subtracting the x-coordinates: \[ \text{Length of AB} = |3 - (-5)| = |3 + 5| = 8 \]

2. Length of AC (vertical side):

   • Point A: (3, 4)
   • Point C: (-5, 8)

   The length of side AC is calculated by subtracting the y-coordinates: \[ \text{Length of AC} = |8 - 4| = 4 \]

Now, we can calculate the area of the rectangle using the formula: \[ \text{Area} = \text{Length} \times \text{Width} = 8 \times 4 = 32 \]

Thus, the area of rectangle ABCD is 32 square feet.