# 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 $B\left( 0, \sin\theta + \cos\theta \right)$ ?

#### 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?

#### APPEARS IN

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