Math Problem Statement

Write the coordinates of the vertices after a reflection over the x-axis.

Solution

The task asks to reflect the coordinates of the vertices TT, UU, VV, and WW over the x-axis. Let's first find the original coordinates of these points:

  • TT: (6,4)(-6, -4)
  • UU: (6,2)(-6, -2)
  • VV: (4,2)(-4, -2)
  • WW: (4,4)(-4, -4)

To reflect a point over the x-axis, the y-coordinate is multiplied by 1-1, while the x-coordinate remains the same. Applying this transformation:

  1. T(6,4)T(6,4)T(-6, -4) \rightarrow T'(-6, 4)
  2. U(6,2)U(6,2)U(-6, -2) \rightarrow U'(-6, 2)
  3. V(4,2)V(4,2)V(-4, -2) \rightarrow V'(-4, 2)
  4. W(4,4)W(4,4)W(-4, -4) \rightarrow W'(-4, 4)

Thus, the reflected coordinates are:

  • T(6,4)T'(-6, 4)
  • U(6,2)U'(-6, 2)
  • V(4,2)V'(-4, 2)
  • W(4,4)W'(-4, 4)

Let me know if you want any further details or clarifications.

Here are 5 related questions:

  1. What happens when reflecting a point over the y-axis?
  2. How do we reflect a point over the line y=xy = x?
  3. Can you explain how to reflect a point over the origin?
  4. How would the reflection change if it was over the line y=xy = -x?
  5. How do translations differ from reflections?

Tip: When reflecting points, always remember that only one coordinate changes: for x-axis reflections, it's the y-coordinate, and for y-axis reflections, it's the x-coordinate.

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Math Problem Analysis

Mathematical Concepts

Geometry
Coordinate Reflections

Formulas

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

Theorems

Reflection Theorem

Suitable Grade Level

Grades 6-8