Question

If co-ordinate axes are rotated through an angle 45⁰ in anticlockwise direction then co-ordinates of point (–1, 1) w.r.t. new system will be–

• A. $\left( \sqrt{2},0 \right)$
• B. $\left( 1,\sqrt{2} \right)$
• C. $\left( 0,\sqrt{2} \right)$
• D. None of these

Answer 1

Answer: (C)

$\left( 0,\sqrt{2} \right)$

Answer 2

\begin{tabular} { | c | c | c | } \hline New & $x = - 1$ & $y = 1$ \ \hline$x ^ { 1 }$ & $\cos 45 ^ { \circ }$ & $\sin 45 ^ { \circ }$ \ \hline$y ^ { 1 }$ & $- \sin 45 ^ { \circ }$ & $\cos 45 ^ { \circ }$ \ \hline \end{tabular}

x¹ = – cos 45⁰ + sin 45⁰ and y¹ = sin 45⁰ + cos 45⁰

x¹ = $- \frac{1}{\sqrt{2}} + \frac{1}{\sqrt{2}}$ y¹ = $\frac{1}{\sqrt{2}} + \frac{1}{\sqrt{2}}$

(0, $\sqrt{2}$)