Using the method of integration, find the area of the triangular region whose vertices are (2, -2), (4, 3) and (1, 2).

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#### Solution

Equation of line AB : -

`y+2=(2+3)/2(x-2)`

⇒ 2y = 5x - 14

Equation of line BC : -

`y-3=1/2(x-4)`

⇒ 3y = x + 5

Equation of line CA : -

(y - 2) = - 4 (x - 1)

4x + y = 6

∴ ar (ΔABC)

`=int_(-2)^3(2y+14)/5dy-int_2^3 3y-5dy`

`=75/5-5/2-24/4`

`=(300-120-50)/20=130/20`

=`13/2`

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