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Coordinate Geometry
CBSE 2026 Board Exam Set 1 (Code 30/7/1)
CBSE_BOARD_PYQ_2026_30_7_1
Grade 10

Question:

[Section C]

The diagonal $BC$ of a rectangle $ABCD$ has endpoints $B(-3, -2)$ and $C(3, 2)$. If the vertex $A$ has coordinates $(3, -2)$, find the coordinates of vertex $D$. Also, find the area of rectangle $ABCD$.

Step-by-Step Solution

Key Concept: Midpoint of diagonal $BC$ equals midpoint of diagonal $AD$.
Midpoint of $BC = \left(\dfrac{-3+3}{2}, \dfrac{-2+2}{2}\right) = (0, 0)$. [1.0 Mark]

Let $D = (x, y)$. Midpoint of $AD = \left(\dfrac{x+3}{2}, \dfrac{y-2}{2}\right) = (0, 0) \Rightarrow D(-3, 2)$. [1.0 Mark]

Length $AB = 6$, Breadth $BC = 4$. Area $= 6 \times 4 = 24$ sq units. [1.0 Mark]

Correct Answer: Coordinates of $D$ are $(-3, 2)$. Area $= 24$ sq units.
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