Question

ABCD is a rectangle where points C and D have coordinates (−2, 0) and (2, 0), respectively. If the area of the rectangle is 24, what is the best way to describe the equation of the line AB?

• A. y = 3
• B. y = 6
• C. y = −3
• D. y = −6

Hint:

For rectangles symmetric about the x-axis, the height determines the vertical location of lines parallel to the base. Use the area formula to calculate dimensions efficiently.

Answer 1

The Correct Option is A

Rectangle Geometry:

Points \(C\) and \(D\) are located on the x-axis at \((-2, 0)\) and \((2, 0)\) respectively. The length of side \(CD\), which serves as the rectangle's base, is calculated as:

\[ \text{Length of } CD = |2 - (-2)| = 4 \]

Rectangle Height Determination: The formula for the area of a rectangle is:

\[ \text{Area} = \text{Base} \times \text{Height} \]

Substituting the known values yields:

\[ 24 = 4 \times \text{Height} \]

Solving for the height gives:

\[ \text{Height} = \frac{24}{4} = 6 \]

Line \(AB\) Identification:

Given that the height is perpendicular to \(CD\) and the rectangle exhibits symmetry about the x-axis, lines \(AB\) and \(CD\) are parallel. Line \(AB\) is positioned 3 units above the x-axis (half of the total height). Therefore, the equation for \(AB\) is:

\[ y = 3 \]

Consequently, the most accurate representation of the equation for \(AB\) is \(y = 3\).