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Question
If the points A (x, y), B (3, 6) and C (−3, 4) are collinear, show that x − 3y + 15 = 0.
Solution
If the given points A (x, y), B (3, 6) and C (−3, 4) are collinear, then
Area of the triangle ΔABC = 0
`therefore 1/2 [x_1(y_2-y_3)+x_2(y_3-y_3)+x_3(y_1-y_2)]=0`
`rArrx(6-4)+3(4-y)+(-3)(y-6)=0`
`rArr2x+12-3y-3y+18=0`
`rArr2x-6y+30=0`
`rArr2(x-3y+15)=0`
`rArrx-3y+15=0`
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