Final answer:
The coordinates of a figure reflected across the y-axis will have their x-coordinates' signs changed while the y-coordinates remain the same. Thus, a point (x, y) becomes (-x, y) after such a reflection.
Step-by-step explanation:
When a figure is reflected across the y-axis, the x-coordinates of the figure's vertices change sign, while the y-coordinates remain the same. This is evident from the coordinates of triangle ABC and its image triangle A'B'C' after the reflection. Looking at the coordinates, we can see that for point A, the x-coordinate changes from 2 to -2, indicating the reflection across the y-axis; however, the y-coordinate remains 3. For point B, the x-coordinate changes from 6 to -6, but the y-coordinate remains 7. Notably, point C does not appear to change, as its x-coordinate is the same in both triangles. This is because point C lies on the y-axis where reflection does not alter its position.
A reflection across the y-axis will therefore result in each point (x, y) of the original figure being transformed to point (-x, y) for the image. This analysis leads us to make the conjecture that the rule for reflecting a point across the y-axis is: if the original point is (x, y), the reflected image will be at (-x, y).