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

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

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

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

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

Prove that the area of any triangle is equal to four times the area of the triangle formed by joining the mid points of its sides.

Statement 1 : The area of the triangle formed by the points A(1000 ,1002),B(1001 ,1004),C(1002 ,1003) is the same as the area formed by the point A^(prime)(0,0),B^(prime)(1,2),C^(prime)(2,1) Statement 2 : The area of the triangle is constant with respect to the translation of axes.

Statement 1: The area of the triangle formed by the points A(1000,1002),B(1001,1004),C(1002,1003) is the same as the area formed by the point A'(0,0),B'(1,2),C'(2,1) statement 2: The area of the triangle is constant with respect to the translation of axes.

Statement 1 : The area of the triangle formed by the points A(1000 ,1002),B(1001 ,1004),C(1002 ,1003) is the same as the area formed by the point A^(prime)(0,0),B^(prime)(1,2),C^(prime)(2,1) Statement 2 : The area of the triangle is constant with respect to the translation of axes.

G is the centroid of the triangle ABC. Prove that the area of the triangle ABG is one third of the area of the triangle ABC.