Question

which figures are translations of figure a? choose all that apply. figure b figure c figure d figure e figure f only choose figures where each vertex of figure a moves the same distance and in the same direction.

Explanation:

Step1: Recall translation definition

A translation moves every vertex of a figure the same distance and in the same direction, preserving shape and size, no rotation/reflection.

Step2: Analyze each figure

- **Figure B**: Has a slanted side (different from A's right angle), so not translation (rotation/change in shape).
- **Figure C**: Shape differs (extra segment? No, wait—check vertices. A's inner square vs C's? Wait, no—A and C: Wait, A's inner part is a square? Wait, no, A has a rectangular extension? Wait, no, looking at the grid: Figure A has a vertical and horizontal segment. Figure C: Does each vertex move same distance? Wait, no—wait, Figure D: Let's check coordinates. Figure A: top-left, top-right, inner, etc. Figure D: same shape, moved down. Figure C: Wait, no, Figure C's inner part is different? Wait, no—wait the key is "each vertex moves same distance and direction".
- **Figure D**: Same shape as A, moved down (vertical translation). Vertices shifted same distance down.
- **Figure E**: Reflected or rotated? Shape different (mirror or rotated), so not translation.
- **Figure F**: Different shape (longer horizontal), so not translation. Wait, original A: let's visualize. Figure A: a sort of "L" with an inner square? Wait, no, the grid: Figure A has a top horizontal, left vertical, bottom horizontal, and an inner vertical and horizontal. Figure D: same structure, moved down. Figure C: wait, maybe I misread. Wait the options: the user's initial check (the purple boxes) were Figure D and F, but that's wrong. Wait no—let's re-express. Translation: same shape, same orientation, only moved. So Figure A, Figure C (wait no, Figure C: does it have the same inner structure? Wait Figure A: top right has a square? Wait no, the figure A: top horizontal, then a vertical down, then a horizontal left, then vertical down? No, looking at the grid: Figure A is a rectangle with a smaller rectangle attached on the right (inner). Figure C: same structure, moved right. Figure D: same structure, moved down. Wait, maybe the correct ones are Figure C and Figure D? Wait the problem's note: "each vertex of figure A moves the same distance and in the same direction". So:
- Figure B: has a slanted side (so shape changed, not translation).
- Figure C: same shape as A, moved right (horizontal translation, same direction, same distance for vertices).
- Figure D: same shape as A, moved down (vertical translation, same direction, same distance).
- Figure E: mirrored (reflection) or rotated, so not translation.
- Figure F: different shape (longer horizontal), so not translation. Wait, maybe I made a mistake. Wait the original figure A: let's see the coordinates. Let's assume grid squares. Figure A: top left (x1,y1), top right (x2,y1), inner top (x3,y2), inner right (x2,y2), bottom right (x2,y3), bottom left (x1,y3), inner bottom (x3,y3), inner left (x1,y2)? No, maybe simpler: Figure A is a shape with a "notch" (the inner square). Figure D: same notch, moved down. Figure C: same notch, moved right. Wait, the initial options: the user's check (the purple boxes) were D and F, but that's incorrect. Wait, maybe the correct answers are Figure C and Figure D? Wait no, let's check the problem again. The question is "Which figures are translations of figure A?". So:

- Figure B: has a diagonal, so not translation (shape changed).
- Figure C: same shape as A, moved right (translation: same orientation, same shape, only position).
- Figure D: same shape as A, moved down (translation).
- Figure E: different orientation (rotated or reflected), so not.
- Figure F: different shape (longer horizontal), so not.

Wait, maybe the initial check (the purple boxes) were wrong, but according to translation definition, Figure C and Figure D are translations. But wait, the user's image: maybe Figure C is a translation (right), Figure D is a translation (down), and Figure A's shape: let's confirm. So the correct figures are Figure C and Figure D? Wait, but the problem's options: the choices are Figure B, C, D, E, F. So according to translation (same shape, same orientation, only moved), the correct ones are Figure C (moved right) and Figure D (moved down). Wait, maybe I misjudged Figure C. Let's see: Figure A and Figure C: do they have the same number of vertices and same connections? Yes. So Figure C is a horizontal translation, Figure D is a vertical translation. Figure B has a diagonal (so a vertex is connected differently), so not. Figure E is a mirror image (reflection), so not. Figure F is stretched (different length), so not. So the correct answers are Figure C and Figure D. But wait, the initial user's check (the purple boxes) were D and F, but that's wrong. Wait, maybe the original figure A is different. Alternatively, maybe the correct answer is Figure C and Figure D. But let's re-express:

Translation: rigid motion, same shape, same size, same orientation, only position changed. So:

- Figure B: orientation changed (diagonal), so no.
- Figure C: same shape, moved right: yes.
- Figure D: same shape, moved down: yes.
- Figure E: orientation changed (rotated/reflected), no.
- Figure F: shape changed (length), no.

So the correct figures are Figure C and Figure D. Wait, but the problem's options: the user's initial check (the purple boxes) were D and F, but that's incorrect. Maybe the user made a mistake. So the correct answer is Figure C and Figure D. But let's check the problem again. The note says "each vertex of figure A moves the same distance and in the same direction". So for Figure C: each vertex moves right by, say, 4 units (same distance, same direction). For Figure D: each vertex moves down by, say, 3 units (same distance, same direction). Figure B: a vertex is connected to a diagonal, so not same shape. Figure E: vertices moved in different directions (reflection), so no. Figure F: vertices moved in different directions (stretched), so no. So the correct answers are Figure C and Figure D.

Answer:

C. Figure C, D. Figure D