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 $\left(y+2\right)=\left(2+\sqrt{3}\right)\left(x+2\right)$