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 after reflecting triangle across the -axis, the reflection rule states that the -coordinate of each point changes its sign, while the -coordinate remains unchanged.
Let the original coordinate of be . After reflection, will have the coordinate .
Evaluate each option:
- Option A: : This suggests was originally at .
- Option B: : This suggests was originally at .
- Option C: : This suggests was originally at .
- Option D: : This suggests was originally at .
Since the reflection only affects the -coordinate, the answer depends on the original coordinates of , which are not directly provided in the problem.
However, assuming 's original coordinates are , the reflection gives .
Final Answer:
C.
Would you like to clarify further steps or confirm initial coordinates?
Here are related questions for further exploration:
- What happens to triangle if reflected across the -axis instead?
- How do coordinates change for a 90-degree rotation around the origin?
- What are the transformations if triangle is translated instead of reflected?
- Can you derive a general formula for reflections across arbitrary lines?
- How does the area of triangle compare to after reflection?
Tip: When reflecting across the -axis, always remember only the -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