Transformations
Grades 8–10 Geometry Graphs
A transformation moves a shape on the plane. Three of them keep the shape identical — only position changes:
- Translation — slide: (x, y) → (x + a, y + b)
- Reflection — flip over an axis: (x, y) → (−x, y) flips across the y-axis
- Rotation — spin around a point: 90° about the origin sends (x, y) → (−y, x)
Those three are rigid — the moved shape is congruent to the original. The fourth kind changes size:
- Dilation — scale: (x, y) → (2x, 2y) doubles everything from the origin
Watch out
"Flip over the y-axis" negates x, not y: (3, 2) → (−3, 2). The
axis you flip over is the coordinate that survives.
Practice
Translate (3, −2) by (+4, +3) → ___
Reflect (5, 4) across the y-axis → ___
Rotate (2, 3) by 90° counterclockwise → ___
Which changes a shape's size?
Next: the Pythagorean theorem · Back: the coordinate plane