Question

The co-ordinate axes are rotated through an angle 135⁰. If the co-ordinates of a point P in the new system are known to be (4, – 3), then the co-ordinates of P in the original system 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. $\left( –\frac{1}{\sqrt{2}},\frac{7}{\sqrt{2}} \right)$

Answer 1

Answer: (B)

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

Answer 2

q = 135⁰ (x¹ , y¹) ŗ (4 , – 3)

x = x¹ cos q – y¹ sin q ; y = x¹ sin q + y¹ cos q