Math Problem Statement
Solve
Solution
The image you uploaded contains several transformation problems involving coordinates and graphs. Let's go through each problem step by step:
Problem 6 (Transformation: Reflection over x-axis)
- Original coordinates of points A, B, C, D for quadrilateral ABCD are:
- A (1, 4)
- B (4, 4)
- C (4, 2)
- D (1, 2)
After reflecting over the x-axis, we change the y-coordinates' sign while keeping the x-coordinates the same. The new coordinates of A'B'C'D' are:
- A' (1, -4)
- B' (4, -4)
- C' (4, -2)
- D' (1, -2)
Problem 7 (Transformation: Reflection over y-axis)
- Original coordinates of points A, B, C, D are:
- A (2, 1)
- B (5, 1)
- C (5, 6)
- D (2, 6)
After reflecting over the y-axis, we change the x-coordinates' sign while keeping the y-coordinates the same. The new coordinates of A'B'C'D' are:
- A' (-2, 1)
- B' (-5, 1)
- C' (-5, 6)
- D' (-2, 6)
Problem 8 (Transformation: Translation by the rule (x, y) → (x + 7, y + 6))
- Original coordinates of points A, B, C, D are:
- A (-8, 5)
- B (-4, 2)
- C (2, -1)
- D (1, -4)
After translating the shape according to the rule, add 7 to the x-coordinate and 6 to the y-coordinate:
- A' (-8 + 7, 5 + 6) = (-1, 11)
- B' (-4 + 7, 2 + 6) = (3, 8)
- C' (2 + 7, -1 + 6) = (9, 5)
- D' (1 + 7, -4 + 6) = (8, 2)
Would you like to go over the details of the transformations or have any specific questions about the graphing?
Additional Questions:
- How does reflection across the x-axis change coordinates?
- How can you verify your translation results on the graph?
- What are other types of transformations besides reflection and translation?
- How do the rules of translation affect the orientation of the shape?
- What happens if you reflect over both axes (x and y) sequentially?
Tip: For reflections, always remember that x-axis affects y-coordinates, and y-axis affects x-coordinates when flipping across these lines!
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Math Problem Analysis
Mathematical Concepts
Geometry
Transformations
Reflections
Translations
Coordinate Plane
Formulas
Reflection over the x-axis: (x, y) → (x, -y)
Reflection over the y-axis: (x, y) → (-x, y)
Translation: (x, y) → (x + a, y + b)
Theorems
Reflection Theorem: Reflecting a point over the x-axis changes the sign of its y-coordinate.
Translation Theorem: Translating a point adds constant values to both x and y coordinates.
Suitable Grade Level
Grades 8-10
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