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If a nebne0, prove that the points (a,a^...

If a `nebne0,` prove that the points `(a,a^(2)),(b,b^(2)),(0,00)` will not be colliear.

Text Solution

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Let the 3 points A `-=(a,a^(2)),B-=(b,b^(2))and C-=(0,0)` from a triangle ABC.
`therefore` Area of `DeltaABC=1/2|a(b^(2)-0)+b(0-a^(2))+0(a^(2)-b^(2))|`
`=1/2[ab^(2)-a^(2)b]=1/2ab(b-a)ne0" "(becauseanebne0)`
So, `DeltaABC` will be formed.
Therefore 3 points A, B and C will not be collinear.
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