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:
- (-8, 3)
- (-7, 3)
- (-5, 5)
- (-4, 8)
Figure C:
- (8, -4)
- (5, -5)
- (3, -7)
- (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:
- (-8, 3) → (8, 3)
- (-7, 3) → (7, 3)
- (-5, 5) → (5, 5)
- (-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:
- (8, 3) → (8, -3)
- (7, 3) → (7, -3)
- (5, 5) → (5, -5)
- (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:
- (8, -3) → (8, -4)
- (7, -3) → (7, -4) → (5, -5)
- (5, -5) → (5, -5)
- (4, -8) → (3, -8)
However, these steps don't align perfectly, suggesting a misunderstanding. A corrected transformation approach:
Correct Sequence:
- Reflection over the y-axis
- Translation down and left
- Verify
Would you like a detailed explanation or have any questions?
Relative Questions:
- How would reflecting over both axes affect a general point (x, y)?
- What is the formula for reflecting a point over the y-axis?
- How can we determine a translation vector given two sets of corresponding points?
- What role does the order of transformations play in getting the correct mapping?
- 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
-
Theorems
-
Suitable Grade Level
High School
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