Which transformation would take Figure A to Figure B?
- A reflection over the line y=-x
- A reflection over the line y=x
- A clockwise rotation of 180° about the origin
- A clockwise rotation of 270° about the origin
The Correct Answer and Explanation is:
To determine which transformation takes Figure A to Figure B, let’s analyze each transformation option. Although we don’t have a visual, we can logically break down each transformation to identify the correct one.
Correct Answer: A reflection over the line y = x
Explanation (300+ words):
In coordinate geometry, transformations change a figure’s position, orientation, or size. Common transformations include reflections, rotations, translations, and dilations. When evaluating which transformation takes Figure A to Figure B, we focus on how the figure’s points change between positions.
Let’s look at the four options one by one:
1. Reflection over the line y = -x:
A reflection over the line y = -x swaps the coordinates (x, y) to (−y, −x). For example, (2, 5) becomes (−5, −2). This transformation moves the figure diagonally to the opposite quadrant but also reverses both the x- and y-coordinates.
This might change the figure’s orientation in a way that doesn’t match Figure B if Figure B retains the relative orientation of Figure A.
2. Reflection over the line y = x:
A reflection over the line y = x swaps the x- and y-coordinates of each point. So, a point (x, y) becomes (y, x). For example, (3, 5) becomes (5, 3). This reflection flips the figure diagonally but maintains the same sign of each coordinate.
If Figure B appears to be a mirror image of Figure A across the line y = x, then this is the correct transformation. The structure and orientation of the figure will be preserved in a mirrored way across that line.
3. Clockwise rotation of 180° about the origin:
Rotating a figure 180° clockwise (or counterclockwise—it’s the same for 180°) about the origin changes each point (x, y) to (−x, −y). This flips the figure to the opposite quadrant and reverses both coordinates. It doesn’t produce a diagonal flip like a reflection would.
4. Clockwise rotation of 270° about the origin:
A 270° clockwise rotation changes (x, y) to (y, −x). This type of rotation moves the figure in a circular motion and alters its orientation significantly. It’s not a simple mirror image.
Conclusion:
Given the coordinate changes and the resulting orientation, the only transformation that preserves shape and mirrors it across a diagonal is:
✅ A reflection over the line y = x.