3.8-02 Homogeneous coordinates in 2D

Homogeneous coordinates in 2D — linear algebra practice

Embed plane points and directions in three-coordinate columns and represent translation with a matrix. Build general affine matrices, calculate outputs, normalize nonstandard homogeneous points and recognize equivalent representatives. The apparent tension between translation and zero preservation is resolved explicitly.

What you will practise

• Encode points and directions
• Build and apply planar affine matrices
• Normalize representatives and interpret the origin

This microlearning belongs to Module 3 of the Complete Linear Algebra Course. Single-select and multiselect questions progress from interpretation to calculation, application and error diagnosis. Each problem is self-contained, and the explanations show how to justify a result rather than only identify a choice. In multiselect tasks, assess each statement separately; the number of correct choices varies.

Before starting, review affine maps and three-by-three multiplication. Work through the reasoning on paper, compare your method with the explanation and revisit the assumptions behind any missed item. These skills prepare you to combine graphics operations within one matrix representation.