Find the equations of the sides of the triangles the coordinates … - Vidyadip

Question

Find the equations of the sides of the triangles the coordinates of whose angular points are respectively: (1, 4), (2, -3) and (-1, -2)

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Answer

Let A(1, 4), B(2, -3) and C(-1, -2)Then the equation of AB is
$\text{y}-\text{y}_=\frac{\text{y}_2-\text{y}_1}{\text{x}_2-\text{x}_1}(\text{x}-\text{x}_1)$
$\text{y}-4=\frac{-3-4}{2-1}(\text{x}-1)$
$\text{y}-4=\frac{-7}{1}(\text{x}-1)$
$\text{7x}+\text{y}=11$
Equation of side BC is
$\text{y}-\text{y}_2=\frac{\text{y}_3-\text{y}_2}{\text{x}_3-\text{x}_2}(\text{x}-\text{x}_2)$
$\text{y}-(-3)=\frac{-2-(-3)}{-1-2}(\text{x}-2)$
$\text{y}+3=\frac{1}{-3}(\text{x}-2)$
$\text{x}+\text{3y}+7=0$
Equation of side AC is
$\text{y}-\text{y}_1=\frac{\text{y}_3-\text{y}_1}{\text{x}_3-\text{x}_1}(\text{x}-\text{x}_1)$
$\text{y}-4=\frac{-2-4}{-1-1}(\text{x}-1)$
$\text{y}-4=3(\text{x}-1)$
$\text{y}-\text{3x}=1$

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