Math Problem Statement

Use the following figure, determine the motion rule that describes the reflection from quadrilateral ABCD to quadrilateral LMNP.

Solution

To determine the motion rule that describes the reflection from quadrilateral ABCDABCD to quadrilateral LMNPLMNP, we need to analyze the figure provided.

Reflection Analysis:

  1. Notice that the quadrilateral ABCDABCD is reflected across the y-axis to form LMNPLMNP.
  2. When reflecting a point across the y-axis, the x-coordinate changes sign, while the y-coordinate remains the same. This transformation rule is: (x,y)(x,y)(x, y) \rightarrow (-x, y)

Final Answer:

The correct motion rule is: (x,y)(x,y)(x, y) \rightarrow (-x, y)


Would you like further clarification or steps for solving reflections? Let me know!

Here are related questions to practice:

  1. How do you determine the motion rule for a reflection across the x-axis?
  2. What is the transformation rule for reflecting across the origin?
  3. How do you reflect a shape across the line y=xy = x?
  4. What changes occur to the coordinates when reflecting over the line y=xy = -x?
  5. How can reflections be combined with translations to describe complex motion?

Tip: To reflect any point across a specific axis, focus on the coordinate that changes based on symmetry!

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Math Problem Analysis

Mathematical Concepts

Reflections
Coordinate Geometry
Transformations

Formulas

Reflection across the y-axis: (x, y) → (-x, y)

Theorems

Coordinate Reflection Rules

Suitable Grade Level

Grades 8-10