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).

Question

Philoid · Accepted 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.