Determine a series of transformations that would map Figure B onto Figure C,

Figure B
1.(-8,3)
2.(-7,3)
3.(-5,5)
4.(-4,8)

To

Figure C
1.(8,-4)
2.(5,-5)
3.(3,-7)
4.((3,-8)

Prompt for correct answer
A  over the  followed by a  over the  .

To determine the series of transformations that map Figure B onto Figure C, let's analyze the points from both figures:

**Figure B:**
1. (-8, 3)
2. (-7, 3)
3. (-5, 5)
4. (-4, 8)

**Figure C:**
1. (8, -4)
2. (5, -5)
3. (3, -7)
4. (3, -8)

### Step 1: Reflection over the y-axis
When you reflect a point over the y-axis, the x-coordinate changes its sign. Let's apply this reflection to the points in Figure B:

1. (-8, 3) → (8, 3)
2. (-7, 3) → (7, 3)
3. (-5, 5) → (5, 5)
4. (-4, 8) → (4, 8)

This reflection brings the x-coordinates closer to those in Figure C, but the y-coordinates need further transformation.

### Step 2: Reflection over the x-axis
Next, reflect the points obtained from the first transformation over the x-axis, which changes the sign of the y-coordinate:

1. (8, 3) → (8, -3)
2. (7, 3) → (7, -3)
3. (5, 5) → (5, -5)
4. (4, 8) → (4, -8)

However, we notice that to achieve the points in Figure C exactly, an additional translation step is required.

### Step 3: Translation
Translate the points by shifting them down by 1 unit:

1. (8, -3) → (8, -4)
2. (7, -3) → (7, -4) → (5, -5)
3. (5, -5) → (5, -5)
4. (4, -8) → (3, -8)

However, these steps don't align perfectly, suggesting a misunderstanding. A corrected transformation approach:

### Correct Sequence:
1. **Reflection over the y-axis**
2. **Translation down and left**
3. **Verify**

Would you like a detailed explanation or have any questions?

### Relative Questions:
1. How would reflecting over both axes affect a general point (x, y)?
2. What is the formula for reflecting a point over the y-axis?
3. How can we determine a translation vector given two sets of corresponding points?
4. What role does the order of transformations play in getting the correct mapping?
5. Can transformations other than reflections and translations map Figure B onto Figure C?

### Tip:
Always check intermediate steps to ensure each transformation aligns with the desired outcome.

Explore how to map Figure B onto Figure C using transformations like reflections and translations. Understand the geometric concepts involved and follow a detailed explanation with step-by-step transformations.

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