Math Problem Statement

The triangle is reflected across the x-axis. What are the vertices of the resulting triangle?

Solution

To solve this reflection problem, let's follow these steps:

  1. Identify the vertices of the original triangle: By examining the image, the vertices of the triangle appear to be:

    • A(6,1)A(-6, 1)
    • B(4,4)B(-4, 4)
    • C(2,1)C(-2, 1)
  2. Reflect each vertex across the x-axis: Reflection across the x-axis changes the y-coordinate of each point to its opposite sign. So, for each vertex (x,y)(x, y), the new point will be (x,y)(x, -y).

    • Reflect A(6,1)A(-6, 1) to get A(6,1)A'(-6, -1)
    • Reflect B(4,4)B(-4, 4) to get B(4,4)B'(-4, -4)
    • Reflect C(2,1)C(-2, 1) to get C(2,1)C'(-2, -1)
  3. Resulting vertices: The vertices of the reflected triangle are:

    • A(6,1)A'(-6, -1)
    • B(4,4)B'(-4, -4)
    • C(2,1)C'(-2, -1)

Thus, the vertices of the triangle after reflection across the x-axis are:

  • (6,1)(-6, -1)
  • (4,4)(-4, -4)
  • (2,1)(-2, -1)

Would you like further explanation on reflections or transformations?

Additional Questions

  1. How would the reflection change if the triangle were reflected across the y-axis?
  2. What are the coordinates if the triangle is reflected across the line y=xy = x?
  3. How would you calculate the reflection if it was across the line y=xy = -x?
  4. How do transformations affect the area of geometric shapes?
  5. How would you find the distance between corresponding points of the original and reflected triangles?

Tip

Remember, reflecting across the x-axis only affects the y-coordinates, while reflecting across the y-axis only affects the x-coordinates.

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Math Problem Analysis

Mathematical Concepts

Geometry
Transformations
Reflections

Formulas

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

Theorems

Reflection Theorem

Suitable Grade Level

Grades 6-8