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`
Concept: Area of the Region Bounded by a Curve and a Line
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