Find the equations of the sides of the triangle, the coordinates of whose vertices are (1, 4), (2, -3) and (-1, -2).
$[3 M a r k]$

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Solution

If $A (x_{1}, y_{1})$ and $B (x_{2}, y_{2})$ be two points, then the equation of line will be,

$(y - y_{1}) = (\frac{y_{2} - y_{1}}{x_{2} - x_{1}}) (x - x_{1})$

Equation of AB,

$y - 4 = \frac{(- 3 - 4)}{(2 - 1)} (x - 1)$
$\Rightarrow y - 4 = - 7 (x - 1)$
$\Rightarrow y - 4 = - 7 x + 7$
$\Rightarrow 7 x + y - 11 = 0$
$[1 M a r k]$

Equation of BC,

$y + 3 = \frac{(- 2 + 3)}{(- 1 - 2)} (x - 2)$
$\Rightarrow y + 3 = \frac{- 1}{3} (x - 2)$
$\Rightarrow 3 y + 9 = - x + 2$
$\Rightarrow x + 3 y + 7 = 0$

$[1 M a r k]$
Equation of AC,

$y - 4 = \frac{(- 2 - 4)}{(- 1 - 1)} (x - 1) \Rightarrow y - 4 = 3 (x - 1) \Rightarrow y - 4 = 3 x - 3 \Rightarrow 3 x - y + 1 = 0$
$[1 M a r k]$

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