Question -
Answer -
Given:
The points (2, 3), (5, 7), and (-3, -1).
The area of triangle with vertices (x1, y1),(x2, y2), and (x3, y3) is
= ½ [x1(y2 – y3) + x2(y3 -y1)+ x3(y1 – y2)]
The area of given triangle = ½ [2(7+1) + 5(-1-3) – 3(3-7)]
= ½ [16 – 20 + 12]
= ½ [8]
= 4
Origin shifted to point (-1, 3), the new coordinates of thetriangle are (3, 0), (6, 4), and (-2, -4) obtained from subtracting a point(-1, 3).
The new area of triangle = ½ [3(4-(-4)) + 6(-4-0) – 2(0-4)]
= ½ [24-24+8]
= ½ [8]
= 4
Since the area of the triangle before and after thetranslation after shifting of origin remains same, i.e. 4.
∴ We cansay that the area of a triangle is invariant to shifting of origin.