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The vertices of a triangle are A(1, 4), B(2, 3) and C(1, 6). Find equations of the sides.

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Equation of the line in two point form is \(\frac {y-y_1}{y_2-y_1} = \frac {x-x_1}{x_2-x_1}\)

Equation of side AB is \(\frac {y-4}{3-4} = \frac {x-1}{2-1}\)

y – 4 = -1(x – 1) 

y – 4 = -x + 1 

x + y = 5

Equation of side BC is \(\frac {y-3}{6-3} = \frac {x-2}{1-2}\)

-1(y – 3) = 3(x – 2) 

-y + 3 = 3x – 6 

∴ 3x + y = 9

Since both the points A and C have same x co-ordinates i.e. 1 

the points A and C lie on a line parallel to Y-axis. 

∴ The equation of side AC is x = 1.

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