Math Problem Statement

Write a rule to describe the transformation.

Solution

The transformation shown in the image appears to be a reflection. To determine the correct reflection, let's analyze the coordinates:

  1. The original shape (black) is reflected to the new shape (blue).
  2. The transformation switches the signs of both x and y coordinates.
  3. This corresponds to a reflection across the line y=xy = -x, where the transformation rule is (x,y)(y,x)(x, y) \rightarrow (-y, -x).

The correct answer is C) reflection across y=xy = -x.

Would you like a step-by-step explanation of how to determine reflections?

Related Questions:

  1. How do you determine the reflection of a point across a given line?
  2. What are the general transformation rules for reflections?
  3. How can you verify a transformation using coordinate pairs?
  4. What is the difference between reflections across y=xy = x and y=xy = -x?
  5. Can reflections be combined with other transformations like rotations?

Tip:

To quickly check if a reflection is across y=xy = x or y=xy = -x, swap the coordinates and observe the sign change.

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Math Problem Analysis

Mathematical Concepts

Transformations
Reflections
Coordinate Geometry

Formulas

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

Theorems

Reflection Theorem

Suitable Grade Level

Grades 8-10