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

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 the axes.

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

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

If the slope of a line is not defined then the line :

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

Name two invariant points under reflection in the x-axis.

Verify that the area of the triangle with vertices (4,6),(7,10) and (1,-2) remains invariant under the translation of axes when the origin is shifted to the point (-2,1) .

Verify that the area of the triangle with vertices (4,6), (7,10) and (1,-2) remains invariant under the translation of axes when the origin is shifted to the point (-2,1).