Find the equations to the sides of the triangles the coordinates of whose angular points are respectively: (i) (1, 4), (2, -3) and (-1, -2) (ii) (0, 1), (2, 0) and (-1, -2)

   

Given:

Points A (1, 4), B (2, -3) and C (-1, -2).

Let ,

   

be the slope of the sides AB, BC and CA,

respectively.

Hence,

The equation of the line passing through the two points:

   

Then,

   

   

and

   

therefore, the equation of the sides AB, BC and CA are

By using the formula,

   

   

or,

   

   

   

or,

   

or,

   

   

and

   

or,

   

   

now, we have

   

or,

   

   

∴ The equation of sides are:

   

or,

   

or,

   

 

 

   

Given:

Points A (0, 1), B (2, 0) and C (-1, -2).

Let us assume,

   

be the slope of the sides AB, BC and CA

hence,

The equation of the line passing through the two points :

   

Then,

   

next,

   

and,

   

So, the equation of the sides AB, BC and CA are

According to formula,

   

or,

   

or,

   

or,

   

or,

   

or,

   

or,

   

or,

   

or,

   

or,

   

now, we have

   

or,

   

or,

   

∴ The equation of sides are:

   

or,