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🔄 Translations, Rotations, and Reflections

Master the three rigid transformations — slide a shape, flip it, and turn it — and describe each move precisely on the coordinate grid.

lessons

~15 min

to learn

🔢 Math

subject

Teens

level

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What you’ll learn

Slides, Flips, and TurnsDistinguish translations, reflections, and rotations and apply translations on a grid.A transformation moves a shape to a new position. Translations, reflections, and rotations are rigid, so the image is always congruent to the original. A translation slides every point the same way, keeping the shape's orientation. A reflection flips it across a mirror line into a mirror image. A rotation turns it about a centre. Recognising each move is the first skill.
Rotations and Combining MovesDescribe rotations by centre, angle, and direction, and apply rotation rules about the origin.A rotation turns a shape about a fixed centre and is described by its centre, angle, and direction. About the origin, the coordinates follow set rules: 90° counterclockwise sends (x, y) to (−y, x), 180° sends it to (−x, −y), and 270° counterclockwise sends it to (y, −x). All three transformations keep a shape congruent; only reflections reverse it into a mirror image.

Questions this course answers

What do translations, reflections, and rotations all have in common?

All three are rigid transformations, so the image is always congruent — the same size and shape as the original.

Translate the point (2, 3) right 4 and up 1. Where does it land?

Add the vector to the point: (2 + 4, 3 + 1) gives (6, 4).

A transformation that flips a shape into a mirror image across a line is a...

Flipping a shape across a mirror line to produce a mirror image is a reflection.

To describe a rotation fully, which three things do you need?

A rotation is defined by its centre of rotation, its angle of turn, and its direction (clockwise or counterclockwise).

Rotate the point (3, 2) by 180° about the origin. What is its image?

A 180° rotation about the origin sends (x, y) to (−x, −y), so (3, 2) becomes (−3, −2).

Which transformation changes a shape's orientation by turning it, without flipping it?

A rotation turns the shape about a centre, changing its orientation without creating a mirror image.

Grounded in trusted sources

Khan Academy — rigid transformations
National Council of Teachers of Mathematics
BBC Bitesize — transformations
Britannica — transformation (geometry)

Every Wunder lesson is built from real, reputable sources — never invented.

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