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 $\overline{AB}$?

Accepted Answer

C. The points $C(-2,0)$ and $D(2,0)$ lie on the x-axis, so the length of side $CD = 2 - (-2) = 4$. Since area of rectangle = $	ext{length} 	imes 	ext{breadth} = 24$, the side $AD = BC = \frac{24}{4} = 6$. Since $CD$ lies on the horizontal line $y=0$, the side $AB$ must be parallel to $CD$ at a vertical distance of 6 units. Thus, the equation of the line $\overline{AB}$ can be $y = 6$ or $y = -6$. Among the choices, $y = 6$ is given.

Rectangle Line Equation

Explanation

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