First slide

Equation of line in Straight lines

Question

The vertex of an equilateral triangle is at (2, –1) and the side opposite to it has the equation x + y = 2 then orthocentre of the traingle is

Easy

A

$(\frac{1}{3}, \frac{1}{3})$
B

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

$(\frac{7}{3}, \frac{- 2}{3})$
D

(1, 1)

Solution

The foot of perpendicular of the vertex on the opposite side of the triangle is (h,k)
                 $\frac{h - 2}{1} = \frac{k + 1}{1} = \frac{- (2 - 1 - 2)}{1 + 1}$
                 $D (h, k) = (\frac{5}{2}, \frac{- 1}{2})$
                G divides AD in the ratio 2 : 1
                 $O = G = (\frac{2 (\frac{5}{2}) + 1 (2)}{3}, \frac{- 1 - 1}{3})$
                 $= (\frac{7}{3}, \frac{- 2}{3})$

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