Final coordinates of a point as a result of rotating a point about origin through an angle of - is equivalent to rotating the co-ordinate axes through an angle of -

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Rotation of Axes

Final coordin...

Question

Final coordinates of a point as a result of rotating a point about origin through an angle of $θ$ is equivalent to rotating the co-ordinate axes through an angle of $- θ$ .

True

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

False

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A
True

In both the cases the relative position of the point changes by $θ$ units. So they are equivalent.

Suggest Corrections

Similar questions

Rotating a point about origin through an angle of $θ$ is equivalent to rotating the co-ordinate axes through an angle of $- θ$ .

Q. If a point

P (4, 3)

is rotated through an angle

45^{o}

in anticlockwise direction about origin, then co-ordinates of

P

in new position are :

Q. The point

(4, 1)

undergoes the following three transformations successively:
(I) Reflection about the line

y = x

(II) Translation through a distance

2

units along the positive direction of

x

-axis.
(III) Rotation of coordinate axes through an angle

\frac{π}{4}

about the origin in the clockwise direction.
The final position of the point is given by the coordinates

Q. Keeping the origin fixed, the coordinates axes are rotated through an angle

θ

. If the equation of the line

\frac{x}{a} + \frac{y}{b} = 1

with respect to new axes is

\frac{x}{p} + \frac{y}{q} = 1

, then?

The origin of the co-ordinate axes is shifted to (-1,3) and the axes is rotated through an angle of $90^{\circ}$ in anti-clockwise direction. If (a,b) is the new coordinates of (2,3) in the new coordinate system, then find the value of $2 a^{2} + 3 b^{2}$

Join BYJU'S Learning Program

Final coordinates of a point as a result of rotating a point about origin through an angle of θ is equivalent to rotating the co-ordinate axes through an angle of −θ.

The correct option is A True In both the cases the relative position of the point changes by θ units. So they are equivalent.

Final coordinates of a point as a result of rotating a point about origin through an angle of $θ$ is equivalent to rotating the co-ordinate axes through an angle of $- θ$ .

The correct option is A
True

In both the cases the relative position of the point changes by $θ$ units. So they are equivalent.