Question

If $\mathbf{C}$ be the centroid of the triangle having vertices$\mathbf{}\mathbf{(}\mathbf{3}\mathbf{,}\mathbf{}\mathbf{-}\mathbf{1}\mathbf{)}\mathbf{,}\mathbf{}\mathbf{(}\mathbf{1}\mathbf{,}\mathbf{}\mathbf{3}\mathbf{)}$ and $\mathbf{(}\mathbf{2}\mathbf{,}\mathbf{}\mathbf{4}\mathbf{)}$. Let $\mathit{P}$ be the point of intersection of the lines $\mathit{x}\mathbf{+}\mathbf{3}\mathit{y}\mathbf{-}\mathbf{1}\mathbf{=}\mathbf{}\mathbf{0}\mathbf{}$and$\mathbf{3}\mathit{x}\mathbf{-}\mathit{y}\mathbf{+}\mathbf{1}\mathbf{=}\mathbf{0}$, then the line passing through the points$CandP$ also passes through the point:

• A. $\mathbf{(}\mathbf{-}\mathbf{9}\mathbf{,}\mathbf{}\mathbf{-}\mathbf{7}\mathbf{)}$
• B. $\mathbf{(}\mathbf{-}\mathbf{9}\mathbf{,}\mathbf{}\mathbf{-}\mathbf{6}\mathbf{)}$
• C. $\mathbf{(}\mathbf{7}\mathbf{,}\mathbf{}\mathbf{6}\mathbf{)}$
• D. $\mathbf{(}\mathbf{9}\mathbf{,}\mathbf{}\mathbf{7}\mathbf{)}$

Answer 1

The correct option is B

$\mathbf{(}\mathbf{-}\mathbf{9}\mathbf{,}\mathbf{}\mathbf{-}\mathbf{6}\mathbf{)}$

Explanation for the correct option:

Step1 : To find Co-ordinates of C

Let, $A(3,-1),B(1,3)$ and $C(2,4)$

$$\begin{gathered} C=(\frac{3+1+2}{3},\frac{-1+3+4}{3}) \\ =(2,2) \end{gathered}$$

Step2 : To Find point of intersection of two lines

$x+3y–1=0$and $3x–y+1=0$ is $P(-1/5,2/5).$

Equation of line CP is

$8x-11y+6=0$

Point $(-9,-6)$ lies on CP.

Hence, correct option is (B)