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Coordinate Geometry
NCERT Exemplar
CBSE
Grade 10

Question:

If $A(1, 2), B(4, 3), C(6, 6)$ and $D(3, 5)$ are the vertices of a parallelogram $ABCD$, then the midpoint of diagonal $AC$ is:
(a) $\left(\dfrac{7}{2}, 4\right)$
(b) $\left(4, \dfrac{7}{2}\right)$
(c) $(5, 4)$
(d) $\left(\dfrac{5}{2}, 3\right)$

Step-by-Step Solution

Key Concept: Diagonals of a parallelogram bisect each other.
Midpoint of $AC = \left(\dfrac{1 + 6}{2}, \dfrac{2 + 6}{2}\right) = \left(\dfrac{7}{2}, \dfrac{8}{2}\right) = \left(\dfrac{7}{2}, 4\right)$. [1.0 Mark]

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🎯 Official CBSE Marking Scheme:
Midpoint of diagonal $AC = (7/2, 4)$: 1.0 Mark

Correct Answer: $\left(\dfrac{7}{2}, 4\right)$
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