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  • A toy is placed at (5, 3) on the rod which is fixed by a screw at (2, 0). If the rod is rotated about the screw through an angle of 15° in clockwise direction, find the new position of the toy.

A toy is placed at (5, 3) on the rod which is fixed by a screw at (2, 0). If the rod is rotated about the screw through an angle of 15° in clockwise direction, find the new position of the toy.

Option: 1

\left ( \mathrm{2+\sqrt{2},\frac{3}{2}} \right )


Option: 2

\left ( \mathrm{2+\frac{3\sqrt{6}}{2},\frac{3}{2}} \right )


Option: 3

\left ( \sqrt{2},\frac{3\sqrt{2}}{2} \right )


Option: 4

None of these 


Answers (1)

best_answer

Slope of line \mathrm{A T=\frac{3-0}{5-2}=1}

\mathrm{\therefore \theta = 45^{\circ}}

\theta_{\text {new }}=45^{\circ}-15^{\circ}=30^{\circ}

Equation of line AT' is given by \mathrm{\frac{x-2}{\cos 30^{\circ}}=\frac{y-0}{\sin 30^{\circ}}=r}

\mathrm{r=A T=A T^{\prime}=\sqrt{(5-2)^2+(3-0)^2}=3 \sqrt{2}}

\therefore Coordinates of T' \equiv\left(2+3 \sqrt{2} \times \frac{\sqrt{3}}{2}, 0+3 \sqrt{2} \times \frac{1}{2}\right)

\equiv\left(2+\frac{3 \sqrt{6}}{2}, \frac{3 \sqrt{2}}{2}\right)

 

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mansi

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