3.8-03 Composing graphics transforms

Composing graphics transforms — linear algebra practice

Construct rotations about an off-origin center by translating, rotating and translating back. Work with exact point calculations, full homogeneous matrices, inverse operations and recovered centers. Comparisons of operation order connect the geometric procedure to the affine offset and matrix product.

What you will practise

• Build a center-based transformation chain
• Compute and verify transformed points
• Recover centers and compare compositions

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 planar rotations, affine maps and homogeneous coordinates. 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 design reliable multi-stage graphics transforms.