Coordinate Geometry
RD Sharma
CBSE
Grade 10
Question:
If the points $A(1, 2), O(0, 0)$ and $C(a, b)$ are collinear, then:
(a) $a = b$
(b) $a = 2b$
(c) $2a = b$
(d) $a + b = 0$
Step-by-Step Solution
Key Concept: Slope $OA = \dfrac{2-0}{1-0} = 2$. Slope $OC = \dfrac{b}{a}$. Collinear $\Rightarrow \dfrac{b}{a} = 2 \Rightarrow b = 2a$.
Slope $OA = 2$, Slope $OC = b/a$. Collinear $\Rightarrow b/a = 2 \Rightarrow b = 2a$. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Equating slopes to get $b = 2a$: 1.0 Mark
Correct Answer: $2a = b$
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