Question

correctly select the statement that best represents the figures on the graph.
#6. the pre - image is in quadrant iii.
#7 the orientation of the vertices changed.
#8. the reflection can be represented by $(-x,y)$.
#9. the line of reflection is the x - axis.
#10. the pre - image and image are congruent.
(options for #6 and related: true; false; the pre - image is in quadrant i; false; the pre - image is in quadrant ii; false; the pre - image is in quadrant vi)

Explanation:

• For #6: The pre-image (ABCD) has all vertices with negative x-values and positive y-values, so it is in Quadrant II, not III.
• For #7: Reflection over the x-axis reverses the vertical order of vertices, changing their orientation.
• For #8: The transformation $(-x,y)$ is reflection over the y-axis, but here the transformation is reflection over the x-axis, represented by $(x,-y)$.
• For #9: The pre-image is in Quadrant II, and the image (A'B'C'D') is in Quadrant III, which is a reflection across the x-axis (mirroring over the horizontal axis).
• For #10: Reflections are rigid transformations that preserve size and shape, so pre-image and image are congruent.

Answer:

#6. False; The pre-image is in quadrant II.
#7. True
#8. False
#9. True
#10. True