Rotation: 90 degree counterclockwise/clockwise, 180 degree about the Origin

In this two-day lesson, I explain rotation transformations of a triangle about the origin (0, 0), focusing on 90° clockwise, 90° counterclockwise, and 180° rotations. Using triangle ABC with coordinates A(−3, 5), B(1, −1), and C(2, 3), I guide students step-by-step through how each point changes under rotation. Students learn both the coordinate rules and the associated matrices for each rotation: • 90° clockwise rotation Rule: (x, y) → (y, −x) Matrix: [ 0 1 ] [−1 0 ] • 90° counterclockwise rotation Rule: (x, y) → (−y, x) Matrix: [ 0 −1 ] [ 1 0 ] • 180° rotation Rule: (x, y) → (−x, −y) Matrix: [−1 0 ] [ 0 −1 ] I demonstrate how to use matrix multiplication to transform each vertex of triangle ABC, helping students clearly see the connection between algebra and geometry. Each rotation produces new images of the triangle (A′B′C′ and A″B″C″), making it easy to visualize how shapes move on the coordinate plane. This lesson is ideal for middle school, high school, and college students who want to master transformations using both rules and matrices. Follow along step-by-step with Zoe to build a strong understanding of rotations and matrix transformations.