Math Problem Statement

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 .

Solution

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.

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Math Problem Analysis

Mathematical Concepts

Geometry
Transformations
Reflections
Translations

Formulas

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Theorems

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Suitable Grade Level

High School