Question

The line segment joining $A\left(3,0\right),B\left(5,2\right)$ is rotated about a point A in anticlockwise sense through an angle $\frac{\pi }{4}$ and B move to C. If a point D be the reflection of C in y-axis, then D=

• A. $\left(-3,2\sqrt{2}\right)$
• B. $\left(3,2\sqrt{2}\right)$
• C. $\left(3,-2\sqrt{2}\right)$
• D. $\left(3,8\sqrt{2}\right)$

Answer 1

The correct option is A $\left(-3,2\sqrt{2}\right)$

$A(3,0)$ and $B(5,2)$

Slope of AB$=\frac{2-0}{5-3}=1$

Then, if $\theta$, is the angle made by AB, with positive direction of x-axis, we have $\tan \theta =1$

$\Rightarrow \theta ={45}^o$

Given, AB is rotated by ${45}^o$ to AC

Now AB$=\sqrt{(3-5{)}^2+(0-2{)}^2}=2\sqrt{2}$

So, coordinate of pr w$(3,2\sqrt{2})$

Hence reflection of c in y-axis is $(-3,2\sqrt{2})$.