Which of the following statement is false?
1) The area of a triangle is invariant under the translation of the axes
2) The slope of a straight line is invariant under the translation of the axes
3) The shifting of origin to another point, while changing the direction of the axes, is called translation of axes.
4) If \(f(x, y)=0\) is transformed equation of a curve when the axes are translated to the point \((h, k)\) then the original equation of the curve is \(f(x-h, y-k)=0\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.