Point A(5, 12) is rotated about the origin O | vedclass

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(A) Let the coordinates of point $A$ be $(x, y) = (5, 12)$ and the angle of rotation be $	heta = 30^\circ$.The coordinates $(x', y')$ of the new poin

Vedclass · Accepted Answer

$6\sqrt{3} + \frac{5}{2}$

Vedclass · Answer

(A) Let the coordinates of point $A$ be $(x, y) = (5, 12)$ and the angle of rotation be $	heta = 30^\circ$.The coordinates $(x', y')$ of the new point $B$ after rotation by $	heta$ anticlockwise are given by:$x' = x \cos 	heta - y \sin 	heta$$y' = x \sin 	heta + y \cos 	heta$Substitute the values $x = 5$, $y = 12$, $	heta = 30^\circ$:$y' = 5 \sin 30^\circ + 12 \cos 30^\circ$$y' = 5 \left( \frac{1}{2} ight) + 12 \left( \frac{\sqrt{3}}{2} ight)$$y' = \frac{5}{2} + 6\sqrt{3}$The ordinate of point $B$ is $\frac{5}{2} + 6\sqrt{3}$.

Point $A(5, 12)$ is rotated about the origin $O$ in the $XY$-plane through an angle of $30^\circ$ in the anticlockwise direction to a new position $B$. The ordinate of point $B$ is...

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