Find the coordinates of M in the original sys | vedclass

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

Question

(B) Let the original coordinates be $(x, y)$ and the new coordinates be $(x', y') = (4, -3)$. The rotation angle is $	heta = 135^{\circ}$.The transfo

Vedclass · Accepted Answer

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

Vedclass · Answer

(B) Let the original coordinates be $(x, y)$ and the new coordinates be $(x', y') = (4, -3)$. The rotation angle is $	heta = 135^{\circ}$.The transformation formulas for rotation of axes are:$x = x' \cos 	heta - y' \sin 	heta$$y = x' \sin 	heta + y' \cos 	heta$Given $\cos 135^{\circ} = -\frac{1}{\sqrt{2}}$ and $\sin 135^{\circ} = \frac{1}{\sqrt{2}}$,we substitute these values:$x = 4 \left(-\frac{1}{\sqrt{2}}ight) - (-3) \left(\frac{1}{\sqrt{2}}ight)$$x = -\frac{4}{\sqrt{2}} + \frac{3}{\sqrt{2}} = -\frac{1}{\sqrt{2}}$$y = 4 \left(\frac{1}{\sqrt{2}}ight) + (-3) \left(-\frac{1}{\sqrt{2}}ight)$$y = \frac{4}{\sqrt{2}} + \frac{3}{\sqrt{2}} = \frac{7}{\sqrt{2}}$Thus,the original coordinates are $\left(-\frac{1}{\sqrt{2}}, \frac{7}{\sqrt{2}}ight)$.

Find the coordinates of $M$ in the original system if the point $M$ changes to $(4, -3)$ when the axes are rotated through an angle of $135^{\circ}$.

Similar Questions

Find the new coordinates of the reflection of the point $(2, -1)$ about the $y$-axis,when the axes are rotated by $45^{\circ}$ in the negative direction without shifting the origin.

If the origin is shifted to a point $(h, k)$ by translation of axes in order to make the equation $x^2+5xy+2y^2+5x+6y+7=0$ free from first-order terms,then:

If the origin is shifted to the point $(2, -5)$ and the axes are kept parallel,what will be the new coordinates of the point $(-5, 3)$?

If the equation of a curve $C$ is transformed to $9x^2 + 25y^2 = 225$ by the rotation of the coordinate axes about the origin through an angle $\frac{\pi}{4}$ in the positive direction,then the equation of the curve $C$ before the transformation is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module