Math Problem Statement

Reflect a point across the x-axis and determine the coordinates of the marked point in both the original and final figures.

Solution

The image you uploaded shows a question related to reflecting a point across the x-axis and then determining the coordinates of the marked point in both the original and the final figures.

To solve this:

  1. Identify the coordinates of the marked point in the original figure. From the graph, it looks like the point is at (3, 4) (x = 3, y = 4).
  2. Reflecting across the x-axis involves changing the sign of the y-coordinate, while the x-coordinate remains the same. So, reflecting (3, 4) across the x-axis will give the point (3, -4).
  3. Coordinates in the original figure: (3, 4)
  4. Coordinates in the final figure (after reflection): (3, -4)

Let me know if you need further clarification or have additional questions!

Here are 5 related questions you might find interesting:

  1. What happens if the point is reflected across the y-axis instead of the x-axis?
  2. How do reflections work when applied to shapes, not just points?
  3. What is the general rule for reflecting a point over any horizontal or vertical line?
  4. How can you use transformations to prove that two shapes are congruent?
  5. What are other types of transformations besides reflections?

Tip: When reflecting a point over the x-axis or y-axis, just remember that only the sign of the corresponding coordinate changes, making it a straightforward process to follow.

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Math Problem Analysis

Mathematical Concepts

Coordinate Geometry
Reflections
Transformations

Formulas

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

Theorems

Reflection Theorem

Suitable Grade Level

Grades 6-9