1.

Prove that the area of triangle remains invariant on transforming the axes.

Answer»

SOLUTION :Let `A(x_(1),y_(1))`, `B(x_(2),y_(2))` and `C(x_(3),y_(3))` are the VERTICES of `DeltaABC`.
`:. "Area of" DeltaABC`
`DELTA=(1)/(2)[x_(1)(y_(2)-y_(3))+x_(2)(y_(3)-y_(1))+x_(3)(y_(1)-y_(2))]` ……..`(1)`
Let origin is shifted to the point `(h,k)`.
Now, the new co-ordinates of the vertices
`A(x_(1)-h,y_(1)-k)`, `B(x_(2)-h,y_(2)-k)`, `C(x_(3)-h,y_(3)-k)`


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