First slide

Equation of line in Straight lines

Question

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

Moderate

A

$2 x - 9 y = 7$
B

$2 x - 9 y - 11 = 0$
C

$2 x + 9 y - 11 = 0$
D

$2 x + 9 y + 7 = 0$

Solution

The coordinates of $S$ are
$(\frac{6 + 7}{2}, \frac{- 1 + 3}{2}) = (\frac{13}{2}, 1)$
Slope of $P S = \frac{1 - 2}{\frac{13}{2} - 2} = - \frac{2}{9}$
Equation of a line passing through $(1, - 1)$ and parallel to $P S$ is
$y + 1 = - \frac{2}{9} (x - 1) \Rightarrow 2 x + 9 y + 7 = 0$

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