Prove that area of a triangle invariant under translation of axes.

Prove that the slope of a straight line is invariant under the translation of axes.

Verify that the area of the triangle with vertics (2, 3), (5, 7) and (-3, -1) remains invariant under the translation of axes when the origin is shifted to the point (-1, 3).

Show that a median of a triangle divides it into two triangles of equal areas.

Prove the theorem of parallel axes.

Statement I : The area of the triangle formed by the points A(100, 102), B(102, 105), C(104, 107) is same as the area formed by A'(0, 0), B' (2, 3), C'(4, 5). Statement II : The area of the triangle is constant wih respect to translation.

The medians BE and CF of a triangle ABC interesct at G. Prove that the area of triangleGBC = area of the quadrilateral AFGE.

If triangle be the area of the triangle, find the area of te triangle whose each side is doubled.

Prove that the area of right-angled triangle of given hypotenuse is maximum when the triangle is isosceles.

True/False: If 'triangle' be the area of the triangle, then the area of the triangle whose each side is doubled is 4 triangle.