Question

The area of the triangle formed by the vertices (1, 1), (2, 2) and (3, 3) is ___ sq. units.

Answer 1

The area of triangle with vertices $(x_1,y_1),(x_2,y_2)and(x_3,y_3)is\frac{1}{2}\left[x_1\right(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2\left)\right].$
Substituting the vertices in the area formula we get,
$=\frac{1}{2}\left[1\right(2-3)+2(3-1)+3(1-2\left)\right].=\frac{1}{2}[-1+4-3].=0sq.unit.$