Question

The point $(4,1)$ undergoes the following three transformations successively
i) Reflection about the line $y=x$
ii) Transformation through a distance of $2$ units along the $+ve$ direction of the x-axis
iii) Rotation through an angle $\frac{\pi }{4}$ about the origin in the anticlockwise direction. The final position of the point is given by the co-ordinates

• A. $\left(\frac{-1}{\sqrt{2}}\frac{7}{\sqrt{2}}\right)$
• B. $(-2,7\sqrt{2})$
• C. $\left(\frac{7}{\sqrt{2}}\frac{1}{\sqrt{2}}\right)$
• D. $(7,1)$

Answer 1

The correct option is C $\left(\frac{7}{\sqrt{2}}\frac{1}{\sqrt{2}}\right)$

Under the transformation reflection about $y=x$ the new point is $(1,4)$
Under the transformation of shifting it $+2$ units along x-axis the new point is $(1+2,4)=(3,4)$
Under the transformation of rotation of $\frac{\pi }{4}$
$y=-X\sin \theta +y\cos \theta$
$X=\frac{3}{\sqrt{2}}+\frac{4}{\sqrt{2}}=\frac{7}{\sqrt{2}}$
$y=\frac{3}{\sqrt{2}}+\frac{4}{\sqrt{2}}=\frac{1}{\sqrt{2}}$