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Question
Find a relation between x and y if the points (x, y), (1, 2) and (7, 0) are collinear.
Solution
If the given points are collinear, then the area of triangle formed by these points will be 0.
Area of Triangle = `1/2 {x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)}`
Area = `1/2[x(2-0)+1(0-y)+7(y-2)]`
`0=1/2[2x-y+7y-14]`
`0=1/2[2x+6y-14]`
2x+6y-14=0
x+3y-7 =0
This is the required relation between x and y.
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