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

Prove that the area of a triangle is invariant under the translation of the 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. (a) Statement 1 and Statement 2, both are correct. Statement 2 is the correct explanation for Statement 1. (b) Statement 1 and Statement 2, both are correct. Statement 2 is not the correct explanation for Statement 1. (c) Statement 1 is correct but Statement 2 is not correct. (d) Statement 2 is correct but Statement 1 is not correct.

Prove that the area of the equilateral triangle described on the side of a square is half the area of the equilateral triangles described on its diagonal.

Prove analytically that the area of a triangle is four times that of the triangle obtained by joining the mid - points of the sides of the given triangle .

A straight line forms a right angled triangle with the axes of coordinates . If the hypotenuse is 10 unit and the area of the triangle is 24 square unit , find the equation of the straight line.

A straight line forms a right angled triangle with the axes of coordinates . If the hypotenuse is 13 unit and the area of the triangle is 30 square unit , find the equation of the straight line.

Prove that the area of the triangle formed by any tangent to the hyperbola xy=c^(2) and the coordinate axes is constant.

Show thathte coefficients of x^(2),xy and y^(2) "in" ax^(2)+2hxy+by^(2) are invariants under the translatio of axes.

Prove that if the areas of two similar triangles are equal, then they are congruent

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