figure b is the result of a transformation on figure a. which transformation would accomplish this? answer choices: a rotation 180° clockwise about the origin, a translation 8 units down, a reflection over the y - axis, a reflection over the x - axis.

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# Brief Explanations:
- A 180° rotation about the origin: For a point $(x,y)$, rotating 180° about the origin gives $(-x,-y)$. But Figure A (left) and Figure B (right) are symmetric over the $y$-axis? Wait, no—wait, looking at the graph, Figure A is on the left (negative $x$-side) and Figure B on the right (positive $x$-side), symmetric over the $y$-axis? Wait, no, wait: a reflection over the $y$-axis takes $(x,y)$ to $(-x,y)$. Wait, Figure A has points like, say, if a vertex of A is $(-5,2)$, then reflecting over $y$-axis would be $(5,2)$, which matches Figure B. But wait, the options: "A rotation 180° clockwise about the origin"—wait, no, let's check the options again. Wait, the options are:
  - A rotation 180° clockwise about the origin
  - A translation 8 units down
  - A reflection over the $y$-axis
  - A reflection over the $x$-axis

Wait, actually, when you rotate 180° about the origin, a point $(x,y)$ becomes $(-x,-y)$. But in the graph, Figure A and B are symmetric with respect to the $y$-axis? Wait, no, looking at the graph, Figure A is on the left (negative $x$) and Figure B on the right (positive $x$), with the same $y$-coordinates. Wait, no—wait, maybe I misread. Wait, the correct transformation: Let's take a vertex of Figure A. Suppose a vertex of A is at $(-5, 2)$, then a reflection over the $y$-axis would map it to $(5, 2)$, which is a vertex of B. But wait, the option "A rotation 180° clockwise about the origin"—wait, no, 180° rotation would flip both $x$ and $y$ signs. Wait, maybe the correct answer is "A reflection over the $y$-axis"? Wait, no, wait the options: Wait, the first option is "A rotation 180° clockwise about the origin". Wait, let's check the center. The two figures are symmetric with respect to the origin? Wait, no, the origin is the intersection of the axes. Wait, if you rotate Figure A 180° about the origin, each point $(x,y)$ becomes $(-x,-y)$. But in the graph, Figure B is on the positive $x$-side, same $y$-level as A. Wait, maybe the correct answer is "A reflection over the $y$-axis"? Wait, no, the options: Wait, the user's options:

Options:
- A rotation 180° clockwise about the origin
- A translation 8 units down
- A reflection over the $y$-axis
- A reflection over the $x$-axis

Wait, let's analyze each:

1. **Rotation 180° about origin**: For a point $(x,y)$, new point is $(-x,-y)$. So if Figure A has a point $(-5, 3)$, rotating 180° would give $(5, -3)$, but Figure B is at $(5, 3)$, so that's not it.

2. **Translation 8 units down**: Would move all points down, but Figure B is at the same vertical level as A, so no.

3. **Reflection over $y$-axis**: For a point $(x,y)$, new point is $(-x,y)$. So if Figure A has a point $(-5, 3)$, reflecting over $y$-axis gives $(5, 3)$, which matches Figure B's position.

4. **Reflection over $x$-axis**: For a point $(x,y)$, new point is $(x,-y)$. So $(-5, 3)$ becomes $(-5, -3)$, which is not Figure B.

Wait, but the first option is "A rotation 180° clockwise about the origin"—wait, maybe I made a mistake. Wait, the graph: Figure A is on the left (negative $x$), Figure B on the right (positive $x$), and they are symmetric with respect to the $y$-axis. But wait, the option "A rotation 180° about the origin"—no, that would flip both axes. Wait, maybe the correct answer is "A reflection over the $y$-axis"? But wait, the first option is "A rotation 180° clockwise about the origin"—wait, maybe the figure is symmetric about the origin? Wait, no, the origin is the center. Wait, let's look at the graph again. The two triangles are on opposite sides of the $y$-axis, with the same shape and orientation, just mirrored over the $y$-axis. So reflection over $y$-axis. But wait, the options: the first option is "A rotation 180° clockwise about the origin"—wait, maybe the problem's figure is different. Wait, maybe I misread. Wait, the user's image: Figure A is on the left (negative $x$), Figure B on the right (positive $x$), and the origin is the center. Wait, a 180° rotation about the origin would make Figure A's points $(x,y)$ become $(-x,-y)$, but Figure B is $(-x,y)$ (reflection over $y$-axis) or $(x,y)$ (reflection over $y$-axis from $(-x,y)$). Wait, maybe the correct answer is "A reflection over the $y$-axis". But let's check the options again. Wait, the options are:

- A rotation 180° clockwise about the origin
- A translation 8 units down
- A reflection over the $y$-axis
- A reflection over the $x$-axis

Wait, maybe the correct answer is "A reflection over the $y$-axis". But wait, the first option: "A rotation 180° clockwise about the origin"—no, that would invert both coordinates. Wait, maybe the figure is symmetric about the origin, but in the graph, the triangles are on opposite sides of the $y$-axis, same $y$-coordinates. So reflection over $y$-axis. So the correct option is "A reflection over the $y$-axis". Wait, but the first option is "A rotation 180° clockwise about the origin"—maybe I made a mistake. Wait, let's take a point from Figure A. Suppose a vertex of A is at $(-4, 2)$, then rotating 180° about the origin would be $(4, -2)$, but Figure B's vertex is at $(4, 2)$, so that's not it. So reflection over $y$-axis: $(-4, 2)$ becomes $(4, 2)$, which matches. So the correct answer is "A reflection over the $y$-axis". Wait, but the options: the third option is "A reflection over the $y$-axis". So that's the answer.

Wait, but the user's options:

- A rotation 180° clockwise about the origin
- A translation 8 units down
- A reflection over the $y$-axis
- A reflection over the $x$-axis

So the correct answer is "A reflection over the $y$-axis".
# Answer:
A reflection over the $y$-axis

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