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Question
Using the method of integration, find the area of the triangle ABC, coordinates of whose vertices are A (4 , 1), B (6, 6) and C (8, 4).
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Solution
Equation of AB
`y - y_1 = (y_2 -y_1)/(x_2-x_1) (x - x_1)`
`y - 1 = (6-1)/(6-4) (x - 4)`
`y - 1 = 5/2 (x - 4)`
2y - 2 = 5x - 20
`y = (5x)/2 - 9`
Equation of BC
`y - 6 = (4 - 6)/(8 - 6) (x - 6)`
`y - 6 = (-2)/(+2) (x - 6)`
y - 6 = -x + 6
y = -x + 12
Equation of AC
`y - 1 = (4 -1)/(8 - 4) (x - 4)`
`y -1 = 3/4 (x - 4)`
`4y - 4 = 3x - 12`
`y = (3x)/4 - 2`
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