Question

Reflecting the point (2, –1) about y-axis, coordinate axes are rotated at $45^{o}$angle in negative direction without shifting the origin. The new coordinates of the point are

• A. $\left( \frac{- 1}{\sqrt{2}},\frac{- 3}{\sqrt{2}} \right)$
• B. $\left( \frac{- 3}{\sqrt{2}},\frac{1}{\sqrt{2}} \right)$
• C. $\left( \frac{1}{\sqrt{2}},\frac{3}{\sqrt{2}} \right)$
• D. None

Answer 1

Answer: (A)

$\left( \frac{- 1}{\sqrt{2}},\frac{- 3}{\sqrt{2}} \right)$

Answer 2

The new position after reflection is (–2, –1)

Rotation makes it

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