You trace the letter 'b' on paper, then fold the paper over a vertical line so the tracing flips to the other side. What does the result look like?
Ab — unchanged, because folding preserves the shape
Bd — a mirror image where the bump faces the other direction
Cq — the letter rotated 180°
Dp — the letter both flipped and rotated
Folding paper over a line is exactly what a reflection does — it produces a mirror image. The letter 'b' reflected over a vertical line becomes 'd': the bump that faced right now faces left. The shape, size, and proportions are perfectly preserved — only the left-right orientation is reversed. 'q' would require a 180° rotation, and 'p' would require both a reflection and a rotation.
Question 2 Multiple Choice
Which of the following is true about both reflections AND rotations?
ABoth transformations change the size of the shape
BBoth flip the shape so it becomes a mirror image
CBoth preserve the shape's size and angle measurements
DBoth require a line of symmetry through the shape
Both reflections and rotations are rigid motions (isometries) — the shape moves without any stretching, shrinking, or distortion. Side lengths and angles are perfectly preserved. This is what distinguishes them from scaling (which changes size). Reflections produce a mirror image; rotations tilt without flipping — but in both cases, the shape itself is completely unchanged. Only its position or orientation in space differs.
Question 3 True / False
After reflecting a triangle over a line, the triangle's side lengths change because the shape has been flipped.
TTrue
FFalse
Answer: False
Reflection is a rigid motion — it preserves all distances and angles exactly. A reflected triangle is congruent to the original: same side lengths, same angles, same area. 'Flipping' describes the orientation change (left-right reversal), not a change in the shape's measurements. If the measurements changed, it would no longer be a reflection — it would be a distortion or stretch.
Question 4 True / False
For a square, rotating it 90° around its center produces a result that looks exactly the same as the original — indistinguishable from no transformation at all.
TTrue
FFalse
Answer: True
A square has 4-fold rotational symmetry: rotating it 90°, 180°, or 270° around its center produces an image identical to the original because all four sides and angles are equal. This is a property of the square's symmetry, not of rotation in general. A rectangle rotated 90° (that is not a square) would look different — it would appear to be lying on its side. The symmetry of the shape determines whether a rotation is 'invisible.'
Question 5 Short Answer
How can you tell whether a shape has been reflected or rotated? What is the key difference to look for?
Think about your answer, then reveal below.
Model answer: After a reflection, the shape is a mirror image — it appears flipped. An asymmetric shape like the letter 'b' becomes 'd' after a horizontal reflection: left and right are swapped. After a rotation, the shape is tilted at an angle but not flipped — 'b' rotated 180° becomes 'q', which is upside-down but not mirrored. A practical test: place a tracing of the original on top of the transformed shape. If you can match them by spinning the tracing (without lifting and flipping it), it's a rotation. If you must flip the tracing over to match, it's a reflection.
The flip test is the conceptual core of distinguishing these two transformations. Rotations keep the shape in the same 'handedness' — a right-handed glove rotated is still a right-handed glove. A reflection reverses handedness — a right-handed glove reflected becomes a left-handed glove. This concept of handedness (chirality) will become important in higher geometry and in understanding mirror symmetry in the physical world.