Area of a triangle from coordinates, and geometry problems
Find the area of a triangle from the coordinates of its three vertices, and use coordinates to solve geometry problems.
- UK: Year 10
- France: grade 11
- Iran: grade 11
- Afghanistan: grade 10
- Russia: grade 9
Guide
When the vertices are on grid points, put the triangle in a rectangle: its area is the rectangle minus the three right-angled corner triangles. The general formula does the same thing without a drawing: S = 12·|x1(y2 − y3) + x2(y3 − y1) + x3(y1 − y2)|.
If the area is zero, the three points lie on one straight line. That is used to find a missing point.
In a parallelogram the diagonals bisect each other. So the two diagonals have the same midpoint, and the fourth vertex follows from it.