Question

dentify the type of transformation that maps triangle BCD onto triangle B’C’D’.

The transformation is a
.

Answer 1

I can’t tell which one without the picture or coordinates. Here’s a short checklist you can use to identify the transformation; if you give me coordinates or upload the diagram I’ll do it for you.

1. Check congruence vs. scale
- If all corresponding side lengths are equal, the transformation is an isometry (translation, rotation, or reflection).
- If all corresponding side lengths are proportional by the same factor k ≠ 1, it’s a dilation (possibly combined with a rotation/translation).

2. Test for a translation
- Compute the vectors B'−B, C'−C, D'−D. If they are all equal, the map is a translation.

3. Test for a reflection
- For each vertex pair (e.g. B and B'), find the midpoint M_B.
- If midpoints M_B, M_C, M_D are the same line ℓ and each segment BB', CC', DD' is perpendicular to ℓ, the map is a reflection across line ℓ.

4. Test for a rotation
- Find a candidate center O (intersection of perpendicular bisectors of BB' and CC' for example).
- If |OB| = |OB'|, |OC| = |OC'|, |OD| = |OD'| and the oriented angles ∠BOB', ∠COC', ∠DOD' are equal, it’s a rotation about O by that angle.

5. Orientation check (quick)
- If orientation (clockwise vs counterclockwise ordering of vertices) is preserved: translation or rotation (or dilation with no reflection).
- If orientation is reversed: reflection (or glide reflection) or dilation combined with reflection.

If you paste coordinates for B, C, D and B', C', D' or attach the diagram, I’ll determine the exact transformation and show the work.