prove that the area of triangle is invariant under the transformation of the axes .

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Please find below the solution to the asked query:

When you transform axes, you can say that line associated with the old axis gets translated toa new position.And as we know that under a translation, distance between two points remains the same, onlythe position of points is changed. Thus, the line segments are mapped to line segments and atriangle remains the same triangle but shifts its position and hence the area of the triangle remains same after transformation of axes.

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