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.
- إيران: الصف ١١
- أفغانستان: الصف ١٠
- روسيا: الصف ٩
- فرنسا: الصف ١١
- بريطانيا: السنة ١٠
لم يُترجَم هذا المختبر إلى هذه اللغة بعد.
الدليل
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 = ١٢·|x١(y٢ − y٣) + x٢(y٣ − y١) + x٣(y١ − y٢)|.
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.