Question

The point $A (4,1)$ undergoes following transformations successively :
(i) reflection about line $y=x$
(ii) translation through a distance of 3 units in the positive direction of $x$-axis
(iii) rotation through an angle $105^{\circ}$ in anti-clockwise direction about origin $O$.
Then the final position of point $A$ is

• A. $\left(\frac{1}{\sqrt{2}}, \frac{7}{\sqrt{2}}\right)$
• B. $(-2,7 \sqrt{2})$
• C. $\left(-\frac{1}{\sqrt{2}}, \frac{7}{\sqrt{2}}\right)$
• D. $(-2 \sqrt{6}, 2 \sqrt{2})$

Answer 1

Answer: (D)

(i) After reflection about line $y=x$ position of point will be $(1,4)$
(ii) After this step $(4,4)$
(iii) $h =4 \sqrt{2} \cos 150^{\circ}, k =4 \sqrt{2} \sin 150^{\circ}$
$h=-2 \sqrt{6}, k=2 \sqrt{2}$