First slide

Equation of line in Straight lines

Question

P is a point on the line y + 2x = 1, and Q and R are two points on the line 3y + 6x = 6 such that triangle PQR is an equilateral triangle. The length of the side of the triangle is

Moderate

A

$2 / \sqrt{15}$
B

$3 / \sqrt{5}$
C

$4 / \sqrt{5}$
D

None of these

Solution

$The given lines are y + 2 x = 1 and y + 2 x = 2 . The distance$ $between the lines is \frac{(2 - 1)}{\sqrt{5}} = \frac{1}{\sqrt{5}}$
$I n t h e t r i a n g l e \cos e c 60^{0} = \frac{P R}{\frac{1}{\sqrt{5}}}$
The side length (PR) of the triangle is $\frac{1}{\sqrt{5}} cosec 60^{\circ} = \frac{2}{\sqrt{15}}$

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