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

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

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$$y' = -x \sin 	heta + y \cos 	heta$Given $(x', y') = (4, -3)$ and $	heta = 135^{\circ}$,we have:$4 = x \cos 135^{\circ} + y \sin 135^{\circ} = -\frac{x}{\sqrt{2}} + \frac{y}{\sqrt{2}}$$\Rightarrow -x + y = 4\sqrt{2} \quad (i)$$-3 = -x \sin 135^{\circ} + y \cos 135^{\circ} = -\frac{x}{\sqrt{2}} - \frac{y}{\sqrt{2}}$$\Rightarrow x + y = 3\sqrt{2} \quad (ii)$Adding $(i)$ and $(ii)$ gives $2y = 7\sqrt{2} \Rightarrow y = \frac{7}{\sqrt{2}}$.Subtracting $(i)$ from $(ii)$ gives $2x = -\sqrt{2} \Rightarrow x = -\frac{1}{\sqrt{2}}$.Thus,the coordinates in the original system are $(-\frac{1}{\sqrt{2}}, \frac{7}{\sqrt{2}})$.

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

The angle through which the coordinate axes are to be rotated to remove the $xy$ term in the equation $x^2+2xy-y^2=0$ is

If the axes are translated to the orthocentre of the triangle formed by the points $A(7,5), B(-5,-7), C(7,-7)$,then the coordinates of the incentre of the triangle in the new system are

If the axes are rotated through an angle $\theta = \frac{\pi}{3}$ in the clockwise direction with respect to the origin $(0, 0)$,what are the coordinates of the point $(4, 2)$ in the new system?

The transformed equation $3x^2 + 3y^2 + 2xy = 2$,when the coordinate axes are rotated through an angle $45^{\circ}$,is

By shifting the origin to the point $(-1, 2)$ through translation of axes,if $ax^2+2hxy+by^2+2gx+2fy+c=0$ is the transformed equation of $2x^2-xy+y^2-3x+4y-5=0$,then $2(f+g+h)=$

Vedclass Test Series

Exam Paper Generator

Online Exam Module