First slide

Equation of line in Straight lines

Question

If one vertex of an equilateral triangle of side a lies at the origin and the other lies on the line $x - \sqrt{3} y = 0$ , the coordinates of the third vertex are

Moderate

A

$(0, \frac{- a}{2})$
B

(a,0)
C

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

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

Solution

Clearly Q, R are the two positions of the third vertex, $P (a \cos 30^{0}, a \sin 30^{0}), Q (0, a), R (a \cos 30^{0}, - a \sin 30^{0})$
i.e., $P (\frac{\sqrt{3} a}{2}, \frac{a}{2}), Q (0, a) R (\frac{\sqrt{3} a}{2}, \frac{- a}{2})$

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