Introduction to Transformations

Geometry · Axiom Academy

Introduction to Transformations Moving, flipping, turning, and resizing shapes on the coordinate plane A transformation moves or resizes a shape by a rule In geometry, a transformation is a way of moving or changing a figure on the coordinate plane. Think of it like a machine: you feed in a shape, apply a rule, and get out a new shape in a new position — or a new size. The shape you start with is the pre-image ; the shape you get back is the image . There are four main moves. Watch one triangle take a quick tour through all of them — it slides , flips , turns , then resizes . Notice the readout: the first three keep the triangle the same size ( rigid ), and only the last one changes it ( non-rigid ). The next beats slow each move down on its own. Same triangle, four different rules — slide, flip, turn, resize. Translation — slide every point the same way A translation slides the whole figure by one fixed amount and direction — a vector . Watch the triangle glide along the arrow. The dashed original stays put, and the thin guide arrows show every vertex moving by the exact same step: right 9 and down 3 . No turning, no flipping, no resizing. Every point of the figure moves by the same vector — that's a translation. Reflection — flip across a mirror line

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