The coordinate of the image with respect to t | vedclass

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(B) The object is at position $(0, 10)$ cm. The mirror makes an angle of $30^{\circ}$ with the negative $x$-axis,which means it makes an angle of $150

Vedclass · Accepted Answer

$(5, -5 \sqrt{3})$

Vedclass · Answer

(B) The object is at position $(0, 10)$ cm. The mirror makes an angle of $30^{\circ}$ with the negative $x$-axis,which means it makes an angle of $150^{\circ}$ with the positive $x$-axis.Alternatively,the line of the mirror makes an angle of $-30^{\circ}$ with the positive $x$-axis.The object $O$ is at $(0, 10)$. The distance of the object from the mirror is $d = 10 \sin(30^{\circ}) = 5 \, 	ext{cm}$.The image $I$ is formed at the same distance $d = 5 \, 	ext{cm}$ on the other side of the mirror.The angle of the line joining the object and the image with the mirror is $90^{\circ}$.The angle of the line $OI$ with the positive $x$-axis is $30^{\circ} - 90^{\circ} = -60^{\circ}$.The distance $OI = 2d = 10 \, 	ext{cm}$.The coordinates of the image $I$ are $(OI \cos(-60^{\circ}), OI \sin(-60^{\circ}))$.$x = 10 \cos(-60^{\circ}) = 10 	imes (1/2) = 5$.$y = 10 \sin(-60^{\circ}) = 10 	imes (-\sqrt{3}/2) = -5 \sqrt{3}$.Thus,the coordinate of the image is $(5, -5 \sqrt{3})$.

The coordinate of the image with respect to the origin $c$ will be:

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