The coordinate axes are rotated through an an | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Let $(x, y)$ be the coordinates in the original system and $(x', y')$ be the coordinates in the new system after rotation by an angle $	heta = 13

Vedclass · Accepted Answer

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

Vedclass · Answer

(D) Let $(x, y)$ be the coordinates in the original system and $(x', y')$ be the coordinates in the new system after rotation by an angle $	heta = 135^{\circ}$.The transformation equations are:$x' = x \cos 	heta + y \sin 	heta$$y' = -x \sin 	heta + y \cos 	heta$Given $(x', y') = (4, -3)$ and $	heta = 135^{\circ}$,we have $\cos 135^{\circ} = -\frac{1}{\sqrt{2}}$ and $\sin 135^{\circ} = \frac{1}{\sqrt{2}}$.Substituting these values:$4 = x(-\frac{1}{\sqrt{2}}) + y(\frac{1}{\sqrt{2}}) \implies -x + y = 4\sqrt{2} \quad (i)$$-3 = -x(\frac{1}{\sqrt{2}}) + y(-\frac{1}{\sqrt{2}}) \implies -x - y = -3\sqrt{2} \implies x + y = 3\sqrt{2} \quad (ii)$Adding $(i)$ and $(ii)$:$2y = 7\sqrt{2} \implies y = \frac{7\sqrt{2}}{2} = \frac{7}{\sqrt{2}}$Subtracting $(i)$ from $(ii)$:$2x = -\sqrt{2} \implies x = -\frac{\sqrt{2}}{2} = -\frac{1}{\sqrt{2}}$Thus,the original coordinates are $(x, y) = \left(-\frac{1}{\sqrt{2}}, \frac{7}{\sqrt{2}}ight)$.

The coordinate axes are rotated through an angle $135^{\circ}$. If the coordinates of a point $P$ in the new system are known to be $(4, -3)$,then the coordinates of $P$ in the original system are

Similar Questions

If the circle $x^2+y^2+8x-4y+c=0$ touches the circle $x^2+y^2+2x+4y-11=0$ externally and cuts the circle $x^2+y^2-6x+8y+k=0$ orthogonally,then $k=$

To which series does $Catharanthus$ $roseus$ belong?

Viruses behave as non-living entities because outside the host cell they:

If $\left[\begin{array}{rrr}1 & 2 & x \\ 4 & -1 & 7 \\ 2 & 4 & -6\end{array}\right]$ is a singular matrix,then $x$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module