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?
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?
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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.
Updated On: Jan 5, 2025
- y = 3
- y = 6
- y = −3
- y = −6
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The Correct Option is A
Solution and Explanation
Understanding the Geometry of the Rectangle:
\(C\) and \(D\) are on the x-axis with coordinates \((-2, 0)\) and \((2, 0)\). The length of side \(CD\) (the base of the rectangle) is:
\[ \text{Length of } CD = |2 - (-2)| = 4 \]
Determine the Height of the Rectangle: The area of a rectangle is given by:
\[ \text{Area} = \text{Base} \times \text{Height} \]
Substituting the known values:
\[ 24 = 4 \times \text{Height} \]
\[ \text{Height} = \frac{24}{4} = 6 \]
Finding the Line \(AB\):
Since the height is perpendicular to \(CD\) and the rectangle is symmetric about the x-axis, the lines \(AB\) and \(CD\) are parallel. The line \(AB\) lies at a height of \(\frac{6}{2} = 3\) units above the x-axis. The equation of \(AB\) is:
\[ y = 3 \]
Thus, the best description of the equation of \(AB\) is \(y = 3\).
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