Let PS be the median of the triangle with vertices P(2, 2), Q(6, -1) and R(7, 3).

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 $(1, -1)$ band parallel to PS is :

Accepted Answer

Let $P,Q,R,$ be the vertices of $$\Delta PQR$$

Since $PS$ is the median, $S$ is mid-point of $QR$

So, $$S = \left( {{{7 + 6} \over 2},{{3 - 1} \over 2}} \right) = \left( {{{13} \over 2},1} \right)$$

Now, slope of $PS$ $$ = {{2 - 1} \over {2 - {{13} \over 2}}} =  - {2 \over 9}$$

Since, required line is parallel to $PS$ therefore slope of required line $=$ slope of
$PS$

Now, equation of line passing through $(1, -1)$ and having slope $$ - {2 \over 9}$$ is

$$y - \left( { - 1} \right) =  - {2 \over 9}\left( {x - 1} \right)$$

$9y + 9 =  - 2x + 2$

$$ \Rightarrow 2x + 9y + 7 = 0$$

Solutions · 1