Determine whether the point (-3, 2) lies inside or outside the triangle whose sides are given by the equations x + y – 4 = 0, 3x – 7y + 8 = 0, 4x – y – 31 = 0. Solution:

According to ques,:

   

   

And

   

forming a triangle and point (-3, 2)

Let ABC be the triangle of sides AB, BC and CA, whose equations:

   

   

and

   

respectively.

On solving them, we get A (7, – 3), B (2, 2) and C (9, 5) as the coordinates of the vertices.

Let P (− 3, 2) be the given point.

The given point P (− 3, 2) will lie inside the triangle ABC, if

(i) A and P lies on the same side of BC

(ii) B and P lies on the same side of AC

(iii) C and P lies on the same side of ABThus, if A and P lie on the same side of BC, then

   

   

Or ,

   

,

This is false

∴ The point (−3, 2) lies outside triangle ABC.