Question

The point (2,3) undergoes the following three transformation successively, The point (2,3) undergoes the following three transformation successively,

(i) Reflection about the line $y = x$.

(ii) Transformationthrough a distance 2 units along the positive direction of y**-**axis.

(iii) Rotation through an angle of 45^oabout the origin in the anticlockwise direction.

The final coordinates of points are

• A. $\left( \frac{1}{\sqrt{2}},\frac{7}{\sqrt{2}} \right)$
• B. $\left( \frac{- 1}{\sqrt{2}},\frac{7}{\sqrt{2}} \right)$
• C. $\left( \frac{1}{\sqrt{2}},\frac{- 7}{\sqrt{2}} \right)$
• D. None

Answer 1

Answer: (B)

$\left( \frac{- 1}{\sqrt{2}},\frac{7}{\sqrt{2}} \right)$

Answer 2

(i) The new position after reflection is (3,2)

(ii) After transformation, it is (3, 2+ 2), i.e, (3, 4)

(iii) Rotation makes it

$(3\cos 45^{o} - 4\sin 45^{o},3\sin 45^{o} + 4\cos 45^{o})$, i.e. $\left( \frac{- 1}{\sqrt{2}},\frac{7}{\sqrt{2}} \right)$