Math Problem Statement

Use the given information to answer the following questions.

Tony graphs triangle PQR and reflects it across the x -axis to create triangle P′Q′R′

What is the coordinate of P′ ? A.(−3,−2)

B.(−2,3)

C.(3,−2)

D.(2,−3)

Solution

To determine the coordinate of PP' after reflecting triangle PQRPQR across the xx-axis, the reflection rule states that the yy-coordinate of each point changes its sign, while the xx-coordinate remains unchanged.

Let the original coordinate of PP be (x,y)(x, y). After reflection, PP' will have the coordinate (x,y)(x, -y).

Evaluate each option:

  • Option A: (3,2)(-3, -2): This suggests PP was originally at (3,2)(-3, 2).
  • Option B: (2,3)(-2, 3): This suggests PP was originally at (2,3)(-2, -3).
  • Option C: (3,2)(3, -2): This suggests PP was originally at (3,2)(3, 2).
  • Option D: (2,3)(2, -3): This suggests PP was originally at (2,3)(2, 3).

Since the reflection only affects the yy-coordinate, the answer depends on the original coordinates of PP, which are not directly provided in the problem.

However, assuming PP's original coordinates are (3,2)(3, 2), the reflection gives (3,2)(3, -2).

Final Answer:

C. (3,2)(3, -2)

Would you like to clarify further steps or confirm initial coordinates?
Here are related questions for further exploration:

  1. What happens to triangle PQRPQR if reflected across the yy-axis instead?
  2. How do coordinates change for a 90-degree rotation around the origin?
  3. What are the transformations if triangle PQRPQR is translated instead of reflected?
  4. Can you derive a general formula for reflections across arbitrary lines?
  5. How does the area of triangle PQRPQR compare to PQRP'Q'R' after reflection?

Tip: When reflecting across the xx-axis, always remember only the yy-coordinate changes sign.

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Math Problem Analysis

Mathematical Concepts

Geometry
Coordinate Plane
Reflections

Formulas

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

Theorems

Reflection Theorem: When a point is reflected across the x-axis, the y-coordinate changes sign while the x-coordinate remains unchanged.

Suitable Grade Level

Grades 6-8