Answer :

Given:


x + y – 4 = 0, 3x – 7y + 8 = 0, 4x – y – 31 = 0 forming a triangle and point (-3, 2)


To find:


Point (-3, 2) lies inside or outside the triangle


Explanation:


Let ABC be the triangle of sides AB, BC and CA, whose equations x + y 4 = 0, 3x 7y + 8 = 0 and 4x y 31 = 0, 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.


Diagram:



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 AB


Thus, if A and P lie on the same side of BC, then


21 + 21 + 8 – 9 – 14 + 8 > 0


50 × - 15 > 0


- 750 > 0,


Which is false


Hence, the point ( 3, 2) lies outside triangle ABC.


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