Question

Use the drop-down menus below to state the sequence of transformations that maps Figure FF onto Figure GG in the animation below. Then use those transformations to determine: are the two figures congruent? Use the drop-down menus to explain why or why not.
x
y
Figure F
Figure G
Answer
Attempt 1 out of 2
A
followed by a
.
The two figures
congruent because
are used to map Figure F onto Figure G

Answer 1

I don’t have the animation or figure image, so I can’t choose the exact transformations for you. If you can upload a screenshot or give coordinates for corresponding vertices (or describe how Figure G is positioned relative to Figure F), I’ll pick the correct dropdown choices and fill in the sentence.

Meanwhile, here’s a short method you can use to identify the required sequence yourself and to complete the sentence:

1. Try a translation first:
- Pick a clear vertex A of Figure F and the corresponding vertex A' of Figure G.
- Compute the vector v = A' − A. Translate F by v. If the whole figure lands on G, the single transformation is “a translation by vector v.”

2. If translation alone fails, check for a rotation:
- Compare orientation of a segment (for example AB in F and A'B' in G). Measure the angle from AB to A'B' about a likely center (often the origin or a vertex).
- If the angle is 90°, 180°, 270°, etc., the transformation may be “a rotation about (point) by (angle).” Try that rotation on all vertices; if it matches, you’re done.
- If rotation doesn’t match exactly, try a rotation followed by a translation (or vice versa).

3. If one figure is mirrored (left/right reversed), check for a reflection:
- Look for reversed orientation (clockwise vs. counterclockwise ordering of vertices).
- Determine the mirror line (common choices: x-axis, y-axis, y = x, or the perpendicular bisector of a pair of corresponding points).
- A reflection across that line (optionally followed by a translation or rotation) might map F to G.

4. Decide congruence:
- If you can map F onto G using only rigid motions (translations, rotations, reflections), the figures are congruent.
- Fill the sentence like: “A (rotation about (point) by (angle)) followed by a (translation by vector (a,b)). The two figures are congruent because rigid motions (rotation and translation) are used to map Figure F onto Figure G.”

If you post the image or coordinates (for example, F has vertices (1,2),(3,2),(2,4) and G has vertices (−2,1),(0,1),(−1,3)), I will give the exact dropdown choices and the completed congruence sentence.