Q. 135.0( 1 Vote )

Using the method of integration find the area of the triangle ABC, coordinates of whose vertices are A(2, 0), B (4, 5) and C (6, 3). [CBSE 2014]

Answer :

It is given that the vertices are A (2, 0), B (4, 5) and C (6, 3).


Now,


Equation of line segment AB is



=> y – 0 = 5x - 10



Equation of line segment BC is



=> 2y – 10 = -2x + 8


=> 2y = -2x + 18


=> y = -x + 9 …(2)


Equation of line segment CA is



=> -4y + 12 = -3x + 18


=> 4y = 3x - 6


…(3)


Thus,


Area(ΔABC) = Area ABLA + Area BLMCA – Area ACMA






= 13 – 6


= 7 units.

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