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: Use the coordinates of C and D to find the length of the base.
The length of the base CD is the difference in the x-coordinates of C and D: \[ \text{Length of CD} = 2 - (-2) = 4 \]
Step 2: Use the area to find the height.
The area of the rectangle is given by: \[ \text{Area} = \text{Length of CD} \times \text{Height} = 4 \times \text{Height} \] Since the area is 24, we solve for height: \[ 24 = 4 \times \text{Height} \Rightarrow \text{Height} = 6 \]
Step 3: Determine the equation of line AB.
The line AB has a slope of \( \frac{6}{4} = \frac{3}{2} \) (since height = 6, base = 4). Hence, the equation of line AB is \( y = \frac{3}{2}x + c \). By checking the available options, we see that the correct equation is \( 4x + 6y = 24 \).
Final Answer: \[ \boxed{4x + 6y = 24} \]