SMO Open · 9. Areas, coordinates and vectors
Compare areas through common heights and bases, let coordinates handle perpendicularity and area, and use normal vectors for distances and reflections in space.
Find unknown areas and length ratios using same-height and same-base arguments.
Use coordinates, the dot product and the determinant formula for areas in the plane.
Compute distances from a point to a line and to a plane.
Work with planes, normal vectors and reflections in three-dimensional space.