Definition
Transformation
A geometry rule that tells where every point of a figure maps.
What it means
Imagine attaching one rule to the whole shape. The rule acts on every point, not just one corner. One rule might slide the shape, turn it, flip it, or make a same-shaped larger or smaller copy. Looking at what stays the same—such as side lengths, angles, or which way the shape faces—helps you name the transformation.
Remember it
One rule, every point: slide, turn, flip, or resize.
Example
Start with triangle A(1, 1), B(3, 1), C(2, 3). Apply the rule (x, y) → (x + 4, y + 1) to every vertex. The image is A′(5, 2), B′(7, 2), C′(6, 4). This is a translation, which is one kind of transformation.
Watch for
Changing only a triangle’s colour is not a geometric transformation of its points. Moving one drawn corner by hand without giving a rule for every point is also not enough to specify a transformation.
Common mix-up
A translation is one kind of transformation. Transformation is the bigger category; it does not mean “slide” only.
Exact meaning
In geometry, a transformation is a rule that sends every point of a figure to exactly one image point. The rule may move, turn, flip, or resize the figure; the transformation type determines which lengths, angles, orientation, and size stay the same.