Maths / Coordinate Geometry / Distance Formula

QUESTION

Find the distance between $\large (cos\theta,-sin\theta )$ and $\large (-cos\theta,sin\theta ).$

 OPTIONS A. 3 units B. 1 unit C. 2 units D. $\large \sqrt2\;units$
Right Option : C

EXPLANATION
Explain TypeExplanation Content
Text

Let the points $\large (cos\theta,-sin\theta )$ and $\large (-cos\theta,sin\theta ).$ be denoted by A and B respectively. We have

$\large AB^{2}=(-cos\theta -cos\theta )^{2}+\left [ sin\theta -(-sin\theta )^{2} \right ]$

$\large =(-2cos\theta )^{2}+(2sin \theta )^{2}$

$\large =4\;cos^{2}\theta +4\;sin^{2}\theta =4(cos^{2}\theta +sin^{2}\theta )=4$

$\large \Rightarrow \;\;\;AB=2\;\;units$

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