Math Problem Statement

Draw the reflection of the triangle across the x-axis.

Solution

To reflect the triangle across the xx-axis, you need to invert the yy-coordinates of each of the triangle’s vertices, keeping the xx-coordinates the same. Here’s the step-by-step process:

  1. Identify the coordinates of each vertex of the triangle from the graph. For instance, if one vertex is at (x,y)(x, y), reflect it to (x,y)(x, -y).

  2. Apply the reflection:

    • For each vertex (x,y)(x, y) of the triangle, the reflected point will be (x,y)(x, -y).
  3. Plot the reflected points on the graph** below the x-axis in the same xx-positions but opposite yy-positions.

  4. Connect the reflected vertices to form the reflected triangle.

Would you like a more detailed breakdown of each step or further assistance with identifying specific coordinates from the graph?

Here are some related questions to expand your understanding:

  1. How do reflections across different axes affect the coordinates of shapes?
  2. What changes occur when reflecting a shape across the yy-axis instead of the xx-axis?
  3. How can you determine the line of symmetry for a given reflection?
  4. How are reflections in the coordinate plane related to transformations in geometry?
  5. What other types of transformations can be performed on shapes in the coordinate plane?

Tip: When reflecting across the xx-axis, only the yy-coordinate changes sign, making it a straightforward transformation.

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Math Problem Analysis

Mathematical Concepts

Geometry
Reflections
Coordinate Plane

Formulas

Reflection across x-axis: (x, y) -> (x, -y)

Theorems

Reflection Theorem

Suitable Grade Level

Grades 6-8