Question

The shape below is transformed to another shape.

Shape C D E F G H

Which shape could be its image?
Shape C D E F G H

mc019-3.jpg

mc019-4.jpg

mc019-5.jpg

Answer 1

I can’t see the pictures you named. Could you either upload the three option images (mc019-3.jpg, mc019-4.jpg, mc019-5.jpg) or describe each option (orientation, which vertex is where)?

In the meantime, here is a short checklist you can use to decide which option is a valid image under rigid motions (translation/rotation/reflection):

1. Check side lengths and angles
- A rigid motion preserves all side lengths and angles. Make sure the candidate has the same shape (same relative side lengths and angles).

2. Check vertex adjacency and order
- Label sequence around the polygon must match. If the original goes C→D→E→F→G→H around the figure, the image under a rotation or translation will have the same cyclic order (maybe starting at a different vertex). A reflection will reverse the cyclic order (C→H→G→F→E→D).

3. Check orientation (clockwise vs counterclockwise)
- Rotations and translations keep orientation. Reflections reverse it. If the original vertex order is clockwise, the image must be clockwise for a rotation/translation, and counterclockwise for a reflection.

4. Use two reference points to test a rigid motion
- Pick two noncollinear vertices of the original (e.g., C and D). Measure the vector from C to D. In a candidate image, find the corresponding labeled points and see if the vector between them is the same after maybe rotating by a fixed angle or negating (for reflection). If you can find a single rotation+translation (or reflection+translation) that maps those two, check a third point to confirm.

5. Quick visual checks
- If one candidate is a mirrored left-right version of the original and labels run in reverse order, that’s a reflection.
- If it’s turned but labels go in the same direction, that’s a rotation.
- If labels are shifted but all relative positions match exactly, that’s a translation.

If you upload the three option images (or type where each label ends up in each option), I’ll check them and tell you which one is the valid image and why.