Question

Let $PS$ be the median of the triangle with vertices$P(2,2),Q(6,–1)$ and $R(7,3)$. The equation of the line passing through $(1,–1)$ and parallel to $PS$ is

• A. $2x–9y–7=0$
• B. $2x–9y–11=0$
• C. $2x+9y–11=0$
• D. $2x+9y+7=0$

Answer 1

The correct option is D

$2x+9y+7=0$

Explanation for the correct option:

Finding the equation of line parallel to $PS$:

Since $S$ is the mid point of $Q$ and $R$

$$\begin{gathered} \therefore S=\left(\frac{7+6}{2},\frac{3-1}{2}\right) \\ =\left(\frac{13}{2},1\right) \end{gathered}$$

Now, slope of
$$\begin{gathered} PS\left(m\right)=\frac{y_2-y_1}{x_2-x_1} \\ =\frac{2-1}{2-{\displaystyle \frac{13}{2}}} \\ =\frac{-2}{9} \end{gathered}$$
Equation of the line passing through $(1,-1)$ and parallel to $PS$ is
$$\begin{gathered} \begin{array}{rcl}y-(-1)& =& \frac{-2}{9}(x-1)\\ y+1& =& \frac{-2x+2}{9}\\ & \Rightarrow & 9y+9+2x-2=0\end{array} \\ \Rightarrow 2x+9y+7=0 \end{gathered}$$

Therefore, the correct answer is option (D).