Rectangle Line Equation

XAT 2025 · Quantitative Ability & Data Interpretation · Easy · Coordinate Geometry

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

  1. A.

    4x + 6y = 24

  2. B.

    None of the other options is correct.

  3. C.

    y = 6

  4. D.

    x = 6

  5. E.

    x + y = 12

Answer

C

Explanation

The points C(−2,0)C(-2,0) and D(2,0)D(2,0) lie on the x-axis, so the length of side CD=2−(−2)=4CD = 2 - (-2) = 4. Since area of rectangle = length×breadth=24\text{length} \times \text{breadth} = 24, the side AD=BC=244=6AD = BC = \frac{24}{4} = 6. Since CDCD lies on the horizontal line y=0y=0, the side ABAB must be parallel to CDCD at a vertical distance of 6 units. Thus, the equation of the line AB‾\overline{AB} can be y=6y = 6 or y=−6y = -6. Among the choices, y=6y = 6 is given.

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