This is the question:

Find the area of the triangle with vertices (1, -2), (-1, 3), (2, 4).

I have already solved this, however my method seems quite lengthy. I just want to know if there's a better way to do it.

My method:

- Label the vertices a, b and c respectively.
- Find the distance between the vertices using the distance formula.
- Let the largest distance be the 'base' of the triangle.
- Find the gradient of the base, choose one of its verticies, and use the point-gradient formula to get the equation of the line.
- Find the line which cuts through the base, and passes through the opposite vertex. Do this by getting the perpendicular gradient of the base, then using the opposite vertex, find the equation of the line using the point-gradient formula.
- Now we simultaneously solve the equation for the base, and the perpendicular line that cuts it. This will give the point at where the line cuts the base.
- We know where the line cuts the base, so we use that to find the height of the triangle, by finding the distance between the point of intersection and the opposite vertex.
- Now it's just a matter of 1/2 * base * height

Is there a better way?