A line passes through the point (1, 2) and ma | vedclass

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(C) The line passes through $(x_1, y_1) = (1, 2)$ with an inclination $	heta = 60^{\circ}$.The coordinates of points at a distance $r = 3$ from $(x_1

Vedclass · Accepted Answer

$(5/2, 2 + 3\sqrt{3}/2)$

Vedclass · Answer

(C) The line passes through $(x_1, y_1) = (1, 2)$ with an inclination $	heta = 60^{\circ}$.The coordinates of points at a distance $r = 3$ from $(x_1, y_1)$ are given by $(x_1 \pm r \cos 	heta, y_1 \pm r \sin 	heta)$.Substituting the values: $x = 1 \pm 3 \cos 60^{\circ} = 1 \pm 3(1/2) = 1 \pm 3/2$.This gives $x = 1 + 1.5 = 2.5 = 5/2$ or $x = 1 - 1.5 = -0.5 = -1/2$.Similarly,$y = 2 \pm 3 \sin 60^{\circ} = 2 \pm 3(\sqrt{3}/2) = 2 \pm 3\sqrt{3}/2$.Thus,the points are $(5/2, 2 + 3\sqrt{3}/2)$ and $(-1/2, 2 - 3\sqrt{3}/2)$.Comparing with the given options,option $C$ is correct.

$A$ line passes through the point $(1, 2)$ and makes an angle of $60^{\circ}$ with the $x$-axis. The coordinates of the points on this line at a distance of $3$ units from the point $(1, 2)$ are:

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