Math Problem Statement
Solution
The two positions of the triangle on the coordinate grid suggest that the figure has undergone a reflection across the x-axis. The triangle starts in quadrant I, with its topmost point at around (6, 5), and then appears in quadrant IV, flipped upside-down, with its topmost point at around (6, -5). This indicates that the triangle has been reflected over the x-axis.
After the reflection, no other significant transformations seem necessary, as the figure maintains its position in terms of horizontal alignment.
Thus, the correct sequence of transformations is "Reflection across the x-axis, horizontal translation."
Would you like further details or have any questions?
Here are 5 related questions for further practice:
- What is the rule for reflecting a point over the x-axis?
- How does reflecting a figure over the y-axis affect its coordinates?
- What is the difference between rotation and reflection in terms of transformations?
- Can you identify transformations that preserve the orientation of a figure?
- How do you combine multiple transformations into a single operation?
Tip: When reflecting over the x-axis, only the sign of the y-coordinates changes; the x-coordinates remain the same.
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Math Problem Analysis
Mathematical Concepts
Transformations
Reflections
Coordinate Geometry
Formulas
Reflection across the x-axis: (x, y) → (x, -y)
Theorems
Transformation Theorem: Reflections preserve distances and angles.
Suitable Grade Level
Grade 6-8
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