BitWithBite
Geometry · Quick Reference
Transformations Cheat Sheet
In one line: a transformation moves or changes a shape's position, size, or orientation — while often preserving its essential form, letting us describe motion mathematically.
Key Ideas
1Translation. Sliding a shape to a new position without rotating, flipping, or resizing it — every point moves the same distance in the same direction.
2Reflection. Flipping a shape over a line (the line of reflection), creating a mirror image.
3Rotation. Turning a shape around a fixed point (the center of rotation) by a certain angle.
4Dilation. Resizing a shape larger or smaller by a scale factor, centered at a fixed point; angles stay the same but side lengths change proportionally.
5Rigid vs. Non-Rigid Transformations. Translations, reflections, and rotations preserve size and shape (rigid). Dilation changes size, so it is non-rigid.
Worked Examples
A triangle is shifted 3 units right and 2 units up, with no rotation or resizing. What transformation is this?
A translation
A shape is flipped over the y-axis, creating a mirror image. What transformation is this?
A reflection
A triangle with sides 2, 3, 4 is dilated by a scale factor of 3. Find the new side lengths.
New sides: 6, 9, 12
Practice Yourself
A shape slides without turning or flipping. What transformation is this?
Translation
A shape is turned 90° around a fixed point. What transformation is this?
Rotation
A shape is resized larger by a scale factor. What transformation is this?
Dilation
Which transformations are 'rigid' (preserve size)?
Translation, reflection, and rotation