Math Problem Statement

Where will the image of D be located after a reflection over the y-axis?

Solution

In the provided image, the task is to reflect point DD over the yy-axis.

To reflect a point across the yy-axis, we change the sign of the xx-coordinate while keeping the yy-coordinate unchanged. Let's analyze the coordinates of point DD and reflect it.

  1. Coordinates of DD: From the graph, the coordinates of point DD appear to be approximately (2,2)(2, -2).

  2. Reflection over the yy-axis: When reflecting over the yy-axis, the rule is: (x,y)(x,y)(x, y) \rightarrow (-x, y) Applying this rule to the coordinates (2,2)(2, -2), the new coordinates will be: (2,2)(-2, -2)

  3. New Location of DD': After the reflection, the image of point DD will be located at (2,2)(-2, -2).

Let me know if you'd like more details, or if you have any further questions!

Here are some related questions:

  1. How do you reflect a point over the xx-axis?
  2. What are the coordinates of point BB after reflecting over the yy-axis?
  3. What is the general rule for reflecting a point over the origin?
  4. How do reflections affect the shape and size of a geometric figure?
  5. Can you reflect a point over a diagonal line like y=xy = x? If so, how?

Tip: When reflecting over the yy-axis, only the sign of the xx-coordinate changes, not the yy-coordinate.

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Math Problem Analysis

Mathematical Concepts

Coordinate Geometry
Reflections

Formulas

(x, y) → (-x, y) for reflection over the y-axis

Theorems

Reflection Theorem across y-axis

Suitable Grade Level

Grades 7-10