3.2-04 Reflections

Reflections — linear algebra practice

Construct reflections across coordinate axes, both diagonal lines and a general line through the origin. Use parallel and perpendicular components to justify matrices and check outputs. The distinction between reflection through an origin-passing line and an offset affine reflection is part of the progression.

What you will practise

• Track fixed and reversed directions
• Derive arbitrary-line reflections
• Recognize reflection matrices and affine exceptions

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 basis images, dot products and projection onto a direction. 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 reflections with other geometric maps.