Types of Transformations

Pre-Algebra · Axiom Academy

LESSON Types of Transformations Discover how shapes slide, turn, flip, and resize on the coordinate plane — and the simple coordinate rule behind each move. Imagine sliding a book across a table — it moves but keeps facing the same direction. In a translation we shift horizontally (left/right) and vertically (up/down). Watch the whole triangle slide as one rigid piece; each vertex follows the same arrow. To translate a point (x, y) by h units horizontally and k units vertically: Example. Translate (2, 3) by 4 units right and 2 units up: Think of spinning a wheel or turning a doorknob. Common angles are 90° , 180° , and 270° , taken counterclockwise (⟲) or clockwise (⟳). In the animation the triangle pivots about the origin, sweeping out the turn angle — the center never moves. 270° counterclockwise (same as 90° clockwise) Rotate (3, 2) by 90° counterclockwise about the origin. Apply : Like looking in a mirror or folding paper in half. Each point and its image are the same distance from the line of reflection, on opposite sides. Watch the triangle flip across the y -axis: the dashed connectors stay perpendicular to the mirror and equal in length on each side. Reflect (4, 2) over the x -axis. Apply :

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