Question

Answer the following question:

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

Answer 1

The vertices of triangle are A(1, 4), B(2, 3) and C(1, 6).

∴ equation of side AB is

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

∴ y – 4 = –x + 1

∴ x + y = 5

Equation of side BC is

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

∴ y – 3 = – 3x + 6

∴ 3x + y = 9

Equation of side AC is

`(y - 4)/(x - 1) = (6 - 4)/(1 - 1) = 2/0`

∴ 0 = 2x – 2

∴ x = 1

Hence, equations of the sides of the triangle are x + y = 5, 3x + y = 9 and x = 1.