←All concepts
Concept · Geometry & Algebra
Spatial coordinates and symmetry
Practice this concept→
A Geometry & Algebra set, untimed
Named traps
4 ways this goes wrong.
Each is a named misconception the questions are built to catch. Open one for the move that tempts, and the fix.
- 3D distance formula errorErrs applying the 3D distance formula (sign or missing term).→
- 3D reflection negates wrong coordinateNegates the wrong coordinate (y vs z), or negates all, when reflecting across a coordinate plane.→
- 3D symmetry type confusedConfuses reflection across an axis, a plane, and the origin by misreading which coordinates flip sign.→
- Axis vs coordinate plane confusedConfuses lying on an axis with lying in a coordinate plane (e.g. one zero coordinate).→
Key formulas
6- Coordinates of ABB − A (component-wise)magnitude |a| = √ax2 + ay2 (+ az2)
- Dot producta·b = |a||b| cos θ = ax bx + ay by (+ az bz)
- Angle between vectorscos θ = (a·b)/(|a||b|)
- Perpendicular: a·b = 0Parallel/collinear (2D): ax by − ay bx = 0 (components proportional)
- Magnitude of a sum|a+b|2 = |a|2 + 2(a·b) + |b|2
- Projection vector of a onto b((a·b)/|b|2) bscalar projection (a·b)/|b|
Shaky underneath?
If the concept underneath still feels loose, patch it here before coming back to CSCA questions.
FoundationsPrecalculus bridgeAlgebra 2 foundations