Math Problem Statement

Which sequence of transformations describes the movement of the figure on the coordinate grid?

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:

  1. What is the rule for reflecting a point over the x-axis?
  2. How does reflecting a figure over the y-axis affect its coordinates?
  3. What is the difference between rotation and reflection in terms of transformations?
  4. Can you identify transformations that preserve the orientation of a figure?
  5. 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