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What is the Distance Between the Points a ( Sin θ − Cos θ , 0 ) and B ( 0 , Sin θ + Cos θ ) ? - Mathematics

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प्रश्न

What is the distance between the points  \[A\left( \sin\theta - \cos\theta, 0 \right)\] and \[B\left( 0, \sin\theta + \cos\theta \right)\] ?

 
 
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उत्तर

The given points are  \[A\left( \sin\theta - \cos\theta, 0 \right)\] and \[B\left( 0, \sin\theta + \cos\theta \right)\] .

Using distance formula, we have

\[AB = \sqrt{\left[ \left( \sin\theta - \cos\theta \right) - 0 \right]^2 + \left[ 0 - \left( \sin\theta + \cos\theta \right) \right]^2}\]
\[ = \sqrt{\left( \sin\theta - \cos\theta \right)^2 + \left( \sin\theta + \cos\theta \right)^2}\]
\[ = \sqrt{\sin^2 \theta + \cos^2 \theta - 2\sin\theta\cos\theta + \sin^2 \theta + \cos^2 \theta + 2\sin\theta\cos\theta}\]
\[ = \sqrt{2\left( \sin^2 \theta + \cos^2 \theta \right)}\]
\[ = \sqrt{2} \text{ units }  \left( \sin^2 \theta + \cos^2 \theta = 1 \right)\]

Thus, the distance between the given points is \[\sqrt{2}\] units . 
 
 
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अध्याय 6: Co-Ordinate Geometry - Exercise 6.6 [पृष्ठ ६२]

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आरडी शर्मा Mathematics [English] Class 10
अध्याय 6 Co-Ordinate Geometry
Exercise 6.6 | Q 28 | पृष्ठ ६२

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