Find the coordinates of the vertices of a triangle, the equations of whose sides are: (i) x + y – 4 = 0, 2x – y + 3 0 and x – 3y + 2 = 0 (ii) y (t1 + t2) = 2x + 2at1t2, y (t2 + t3) = 2x + 2at2t3 and, y(t3 + t1) = 2x + 2at1t3.

   

and

   

Given:

   

and

   

Let us find the point of intersection of pair of lines.

   

   

And,

   

solving (1) and (2) using cross – multiplication method, we have

   

Solving (1) and (3) using cross – multiplication method, we have

   

Similarly, solving (2) and (3) using cross – multiplication method, we have

x = – 7/5, y = 1/5

∴ The coordinates of the vertices of the triangle are:

   

   

   

and,

   

To find the point of intersection of pair of lines,

   

   

And ,

   

By solving (1) and (2) using cross – multiplication method, we have

Solving (1) and (3) using cross – multiplication method, we have

Solving (2) and (3) using cross – multiplication method, we have

∴ The coordinates of the vertices of the triangle are: