Question

What is the formula of area of triangle in coordinate geometry?

Answer 1

Suppose a triangle has 3 vertices `(x_1, y_1)`, `(x_2, y_2)` and `(x_3, y_3)`

Let `(u_2, v_2) = (x_2-x_1,y_2-y_1)`

and `(u_3, v_3) = (x_3-x_1,y_3-y_1)`

Then area `= abs(u_2v_3-v_2u_3)/2`

Explanation:

If you have come across it, this is half the absolute value of the cross product of two vectors representing two sides of the triangle.