Question

The point (4, 1) undergoes the following three transformations successively.
(i) Reflection about the line y = x
(ii) Transformation through a distance 2 unit along the positive direction of x-axis.
(iii) Rotation through an angle of π/4 about the origin in the anti-clockwise direction.
The final position of the point is given by the coordinates

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

(i) (4, 1) $\to$ (1, 4)
(ii) (1, 4) $\to$ (3, 4)
(iii) $X=xcos{45}^{\circ }–ysin{45}^{\circ }$
$=\frac{1}{\sqrt{2}}(3-4)=-\frac{1}{\sqrt{2}}andY=xsin{45}^{\circ }-ycos{45}^{\circ }=\frac{1}{\sqrt{2}}(3+4)=\frac{7}{\sqrt{2}}Hencepointis(-\frac{1}{\sqrt{2}},\frac{7}{\sqrt{2}})$