Question

ABCD is a rectangle, where the coordinates of C and D are (-2,0) and (2,0), respectively. If the area of the rectangle is 24, which of the following is a possible equation representing the line AB?

• A. \( 4x + 6y = 24 \)
• B. \( x + y = 12 \)
• C. \( x = 6 \)
• D. None of the other options is correct.

Hint:

Use the formula for the area of a rectangle (Area = Length \( \times \) Height) to find unknown dimensions when given the area.

Answer 1

The Correct Option is A

Step 1: Calculate the base length using coordinates C and D.
The length of base CD is the difference in the x-coordinates of C and D:\[\text{Length of CD} = 2 - (-2) = 4\]
Step 2: Determine the height from the area.
The area of the rectangle is calculated as:\[\text{Area} = \text{Length of CD} \times \text{Height} = 4 \times \text{Height}\]Given the area is 24, we solve for the height:\[24 = 4 \times \text{Height} \Rightarrow \text{Height} = 6\]
Step 3: Find the equation of line AB.
Line AB has a slope of \( \frac{6}{4} = \frac{3}{2} \) (derived from height = 6 and base = 4). Therefore, the equation of line AB is of the form \( y = \frac{3}{2}x + c \). Based on the provided options, the correct equation is \( 4x + 6y = 24 \).
Final Answer: \[\boxed{4x + 6y = 24}\]