First slide

Equation of line in Straight lines

Question

A line joining two points A(2, 0) and B(3, 1) is rotated about A in anticlockwise direction through an angle 15°. If B goes to C in the new position, then the coordinates of C are

Moderate

A

$(2, \frac{\sqrt{3}}{2})$
B

$(2, - \frac{\sqrt{3}}{2})$
C

$(2 + \frac{1}{\sqrt{2}}, \sqrt{\frac{3}{2}})$
D

None of these

Solution

Slope of line $A B = \frac{0 - 1}{2 - 3} = = \tan 45^{0}$
$∴ ∠ B A X = 45^{0}$
Given $∠ C A B = 15^{0}$
$∴ ∠ C A X = 60^{0}$
$∴$ Slope of line AC = tan 60º = $\sqrt{3}$
Now, line AC makes an angle of 60° with positive direction of x-axis and $A C = A B = \sqrt{{(3 - 2)}^{2} + {(1 - 0)}^{2}} = \sqrt{2}$
$∴$ Coordinates of C are $(2 + \sqrt{2} \cos 60^{0}, 0 + \sqrt{2} \sin 60^{0})$
i.e., $(2 + \frac{1}{\sqrt{2}}, \sqrt{\frac{3}{2}})$

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