Let's review the image of the test and analyze the answers provided:

1. Problem 1

• Question: Determine the translation that maps Figure D onto Figure C.
• Student Answer: Translation 1 unit right, 8 units up, and 2 units down (correction in the test shows "down" corrected).
• Feedback: The student was marked incorrect here, possibly due to an incorrect direction or distance of translation.

Expected Translation: You would check the grid and adjust the translation to correctly map Figure D to Figure C. Double-check if the movement was over-counted or under-counted.

2. Problem 2

• Question: Determine a series of transformations that would map Figure Q onto Figure R.
• Student Answer: The student mentions translation 5 units left, a reflection over the x-axis, and rotation, but it seems there are corrections, and the answer was marked incorrect.

Expected Answer: The series of transformations may have been out of order or incorrectly applied. Analyzing the figures is necessary to determine the proper transformation series.

3. Problem 3

• Question: Figure V is the result of a transformation on Figure B. Which transformation would accomplish this?
• Student Answer: The student selected option C: Reflection over the x-axis.
• Feedback: This was marked correct, so the transformation was correctly identified as a reflection over the x-axis.

4. Problem 4

• Question: What is the image point of (-8, -5) after the transformation T: (x, y) → (x + 2, -y)?
• Student Answer: (-10, 3) marked incorrect.

Expected Answer: Applying the transformation T to (-8, -5): $x' = x + 2 = -8 + 2 = -6$ $y' = -y = -(-5) = 5$ So the correct point is (-6, 5), not (-10, 3).

5. Problem 5

• Question: What is the image point of (-6, 5) after a translation right 2 units and down 4 units?
• Student Answer: (-10, 7), marked incorrect.

Expected Answer: Translation involves adding to the x-coordinate and subtracting from the y-coordinate: $x' = -6 + 2 = -4$ $y' = 5 - 4 = 1$ The correct answer should be (-4, 1), not (-10, 7).

Would you like further explanation on any of these transformations?

5 Related Questions:

1. How can I double-check translation distances on a grid?
2. What is the effect of combining a reflection and rotation?
3. Can a transformation sequence include both translations and reflections?
4. How do reflections change coordinates on the x-axis and y-axis?
5. How do I apply a translation in general form (x + a, y + b)?

Tip:

When working with transformations, it's helpful to break them down into steps and verify the outcome at each stage before proceeding.