Math Problem Statement

Koordinate?

Führe eine Spiegelung an der y-Achse durch. Bestimme die Koordinaten der Spiegelpunkte.

Solution

The task asks to reflect the points on the grid across the y-axis. When reflecting across the y-axis, the x-coordinate changes sign, while the y-coordinate remains the same.

Here are the steps to calculate the coordinates of the mirror points:

  1. Identify the current coordinates of each point (A, B, C, etc.).
  2. Reflect across the y-axis, changing the sign of the x-coordinates.

Let me start by listing the original coordinates of the points and then reflecting them.

Original Coordinates:

  • A: (2, 1)
  • B: (2, 2)
  • C: (1, 2)
  • D: (0, 2)
  • E: (0, 1)
  • F: (1, 1)
  • G: (2, -3)
  • H: (2, -2)
  • I: (1, -2)
  • J: (0, -3)
  • K: (0, -1)
  • L: (1, -1)
  • M: (0, -2)
  • N: (0, 0)

Reflected Coordinates (Mirror across y-axis):

  • A' = (-2, 1)
  • B' = (-2, 2)
  • C' = (-1, 2)
  • D' = (0, 2)
  • E' = (0, 1)
  • F' = (-1, 1)
  • G' = (-2, -3)
  • H' = (-2, -2)
  • I' = (-1, -2)
  • J' = (0, -3)
  • K' = (0, -1)
  • L' = (-1, -1)
  • M' = (0, -2)
  • N' = (0, 0)

If you need more details or have questions, feel free to ask!

Here are 5 related questions for practice:

  1. What happens to coordinates when reflecting across the x-axis instead of the y-axis?
  2. How would the coordinates change if the reflection was across the line y=xy = x?
  3. Can you reflect any shape across both the x- and y-axis? What would the final coordinates look like?
  4. How do you reflect points across a line that is not vertical or horizontal, such as y=xy = -x?
  5. How would the coordinates of a point change if translated by a certain vector instead of reflecting?

Tip:

When reflecting a point over the y-axis, the y-coordinate stays the same, but the x-coordinate's sign is reversed. This is helpful to remember when reflecting any geometric shapes!

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Math Problem Analysis

Mathematical Concepts

Geometry
Reflections
Coordinate Plane

Formulas

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

Theorems

Reflection Theorem
Coordinate Geometry

Suitable Grade Level

Grades 6-8