Question

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

Answer 1

Vertices of ΔABC are A(1, 4), B(2, 3) and C(1, 6)
Equation of the line in two point form is

`(y - y_1)/(y_2 - y_1) = (x - x_1)/(x_2 - x_1)`

Equation of side AB is

`(y - 4)/(3 - 4) = (x - 1)/(2 - 1)`

∴ `(y - 4)/(-1) = (x - 1)/1`

∴ y – 4 = – 1(x – 1)
∴ x + y = 5
Equation of side BC is

`(y - 3)/(6 - 3) = (x - 2)/(1 - 2)`

∴ `(y - 3)/3 = (x - 2)/(-1)`

∴ – 1(y – 3) = 3(x – 2)
∴ 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.