Math Problem Statement

What is a reflection rule that maps each triangle and its image?

Solution

To solve this reflection problem, we need to identify the line of reflection and the transformation rule that maps one triangle onto the other.

Step-by-Step Solution:

  1. Identify the line of reflection:

    • The line of reflection appears to be the line y=xy = x, as the triangle in blue and the triangle in black are symmetric across this line.
  2. Determine the reflection rule:

    • For a reflection across the line y=xy = x, the coordinates (x,y)(x, y) of any point are transformed to (y,x)(y, x).
    • Therefore, the reflection rule is rt(x,y)=(y,x)r_t(x, y) = (y, x).
  3. Equation of the reflection line:

    • The equation of the line tt is y=xy = x.

Answer:

The reflection rule is: rt(x,y)=(y,x)r_t(x, y) = (y, x) where the equation of line tt is y=xy = x.

Would you like more details on this problem, or do you have any questions?


Related Questions

  1. How do you find the line of reflection when given two shapes?
  2. What are other common reflection rules for different reflection lines?
  3. How does reflecting over y=xy = -x differ from reflecting over y=xy = x?
  4. Can the distance between corresponding points help verify a reflection?
  5. How would this transformation rule change if the line of reflection were horizontal or vertical?

Tip:

When reflecting a point across the line y=xy = x, remember that you simply swap the coordinates of the point.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Geometry
Transformations
Reflections

Formulas

Reflection rule across y = x: (x, y) -> (y, x)

Theorems

Reflection across a line theorem

Suitable Grade Level

Grades 8-10