Math Problem Statement

Answer correctly the exit ticket part

If the figure in the picture is reflected over the x-axis, and point A was at (-1, 4), what are the coordinates of A' after the reflection?

Solution

In the "EXIT TICKET" section, the task asks about the reflection of point A (at (1,4)(-1, 4)) across the x-axis.

When a point is reflected over the x-axis, its x-coordinate stays the same, but the y-coordinate changes its sign. So:

  • The original point is A(-1, 4).
  • After reflecting over the x-axis, the new point will have the same x-coordinate, but the y-coordinate will change to its opposite, resulting in A'(-1, -4).

Thus, the coordinates of point A' after the reflection are (1,4)(-1, -4).

Let me know if you need further clarification or have any other questions! Here are some follow-up questions:

  1. How does reflection work over the y-axis?
  2. What is the effect of reflecting a point across both axes?
  3. Can you describe the symmetry of the x-axis reflection?
  4. How can you perform a reflection over a line other than the axes, like the line y=xy = x?
  5. What is the geometric significance of reflections in coordinate geometry?

Tip: Remember that reflection always involves changing the sign of the relevant coordinate depending on the axis of reflection.

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Math Problem Analysis

Mathematical Concepts

Coordinate Geometry
Reflections

Formulas

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

Theorems

Reflection theorem

Suitable Grade Level

Grades 6-8