Coordinate Geometry
RD Sharma
CBSE
Grade 10
Question:
The distance between the points $(\cos \theta, \sin \theta)$ and $(\sin \theta, -\cos \theta)$ is:
(a) $\sqrt{2}$
(b) $1$
(c) $2$
(d) $2\sqrt{2}$
Step-by-Step Solution
Key Concept: $d^2 = (\cos \theta - \sin \theta)^2 + (\sin \theta + \cos \theta)^2 = 2(\sin^2 \theta + \cos^2 \theta) = 2 \Rightarrow d = \sqrt{2}$.
$d = \sqrt{(\cos\theta - \sin\theta)^2 + (\sin\theta + \cos\theta)^2} = \sqrt{2(\cos^2\theta + \sin^2\theta)} = \sqrt{2}$. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Evaluating distance $= \sqrt{2}$: 1.0 Mark
Correct Answer: $\sqrt{2}$
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