Advertisement Remove all ads

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

Short Note

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

 
 
Advertisement Remove all ads

Solution

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 . 
 
 
  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

RD Sharma Class 10 Maths
Chapter 6 Co-Ordinate Geometry
Q 28 | Page 62
Advertisement Remove all ads

Video TutorialsVIEW ALL [2]

Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×