Math Problem Statement

find the reflection corrdienates

Find the reflection coordinates of points C, D, E, and F over the y-axis.

Solution

To find the reflection coordinates of the points in the image, it is necessary to identify the axis of reflection. Based on the grid, let's assume the reflection occurs over the y-axis (as it’s the most commonly reflected axis in this context).

Here are the current coordinates of the points CC, DD, EE, and FF before reflection:

  • C(6,8)C(-6, -8)
  • D(2,8)D(-2, -8)
  • E(2,2)E(-2, -2)
  • F(6,2)F(-6, -2)

Reflection over the y-axis:

For a reflection over the y-axis, the rule is to negate the x-coordinate while keeping the y-coordinate unchanged. So, the new coordinates after reflection will be:

  • C=(6,8)C' = (6, -8)
  • D=(2,8)D' = (2, -8)
  • E=(2,2)E' = (2, -2)
  • F=(6,2)F' = (6, -2)

These are the reflected coordinates of the points across the y-axis.

Let me know if you'd like further details or clarification.
Here are some questions for expanding your understanding:

  1. What would be the reflection rule for the x-axis instead of the y-axis?
  2. How would you reflect the shape over the line y=xy = x?
  3. What transformations occur if both axes (x and y) are reflected simultaneously?
  4. How can you find the coordinates after a rotation of 90 degrees about the origin?
  5. How can translation be applied to this shape after reflection?

Tip: Reflections across different lines often involve different coordinate rules. Always identify the reflection line first!

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Math Problem Analysis

Mathematical Concepts

Geometry
Coordinate Geometry
Reflections

Formulas

Reflection over the y-axis: (x, y) -> (-x, y)

Theorems

Reflection Theorem

Suitable Grade Level

Grades 6-8