31. A triangle has been moved 3 units left and 2 units down to form a new congruent triangle. If one original vertex was (-3,5), which of the following could be the corresponding vertex?
Answer: C
The corresponding vertex is (-6,3).
After moving the original vertex (-3,5) 3 units left and 2 units down, the new coordinates can be calculated as follows: x-coordinate changes from -3 to -3 - 3 = -6, and the y-coordinate changes from 5 to 5 - 2 = 3. Therefore, the corresponding vertex is (-6,3).
A) (-6,7)
This option is incorrect because, although the x-coordinate is correctly shifted to -6, the y-coordinate has increased to 7 instead of decreasing by 2, which fails to match the transformation applied to the original vertex.
B) (0,3)
This option is also incorrect. While the y-coordinate is correctly at 3, the x-coordinate of 0 does not reflect the necessary leftward shift of 3 units from -3, which should result in -6.
C) (-6,3)
This option is correct as it accurately reflects the transformation applied to the original vertex (-3,5). The x-coordinate has been moved 3 units left to -6, and the y-coordinate has been moved 2 units down to 3, matching the required changes.
D) (5,7)
This option is incorrect since both the x and y coordinates do not correspond to the appropriate shifts. The x-coordinate has moved 8 units to the right instead of 3 units to the left, and the y-coordinate has increased rather than decreased.
Conclusion
The correct answer, (-6,3), accurately reflects the required transformation of moving the original vertex (-3,5) left by 3 units and down by 2 units. All other options fail to meet the criteria for the congruence of the vertex after transformation, either incorrectly shifting the x-coordinate, the y-coordinate, or both.