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Coordinate Geometry

RD Sharma

CBSE

Grade 10

Question:

If $P\left(\dfrac{a}{3}, 4\right)$ is the midpoint of the line segment joining $Q(-6, 5)$ and $R(-2, 3)$, then the value of $a$ is:
(a) $-4$
(b) $-12$
(c) $12$
(d) $-6$

Step-by-Step Solution

Key Concept: Midpoint $x$-coordinate: $\dfrac{a}{3} = \dfrac{-6 - 2}{2} = -4 \Rightarrow a = -12$.

$\dfrac{a}{3} = -4 \Rightarrow a = -12$. [1.0 Mark]

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🎯 Official CBSE Marking Scheme:
Solving $a = -12$: 1.0 Mark

Correct Answer: $-12$

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