Question

In an equilateral triangle $ABC,$ equation of the side $BC$ is $x+y-2=0$ and the centroid of $\Delta ABC$ is $\left(0 , 0\right).$ If points $A, \, B$ and $C$ are in anticlockwise order, then the equation of side $AC$ is

• A. $\left(y + 2\right)=\left(2 - \sqrt{3}\right)\left(x + 2\right)$
• B. $\left(y + 2\right)=\left(2 + \sqrt{3}\right)\left(x + 2\right)$
• C. $\left(y + 1\right)=\left(2 + \sqrt{3}\right)\left(x + 1\right)$
• D. $x+2=0$

Answer 1

Answer: (B)

Foot of $\left(0,0\right)$ on line $BC$ is $D\left(1,1\right)$
Because $\left(0,0\right)$ divides $AD$ internally in the ratio $2:1$
Hence, by using section formula $A\equiv \left(- 2 , - 2\right)$
Slope of $AC$ is $tan \left(45 ^\circ + 30 ^\circ \right)=2+\sqrt{3}$
Equation of $AC$ is $\left(y + 2\right)=\left(2 + \sqrt{3}\right)\left(x + 2\right)$