Question
Point \( P \) is located at \( (6,-5) \). \( P \) is reflected across the \( y \)-axis to create \( P^{\prime} \). What quadrant is \( P^{\prime} \) in? A. I B. II C. III D. IV Please select the best answer from the choices provided
Ask by Willis Chandler. in the United States
Jan 30,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( P' \) is in the third quadrant.
Solution
Point \( P \) is located at \( (6, -5) \). When reflecting a point across the \( y \)-axis, the \( x \)-coordinate changes sign while the \( y \)-coordinate remains the same.
So, the reflected point \( P' \) will have coordinates:
\[
P' = (-6, -5)
\]
To determine the quadrant where \( P' \) lies:
- The \( x \)-coordinate is negative.
- The \( y \)-coordinate is also negative.
Both coordinates being negative places \( P' \) in the **third quadrant**.
**Answer:** C. III
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Bonus Knowledge
When point \( P \) at \( (6, -5) \) is reflected across the \( y \)-axis, the \( x \)-coordinate changes sign while the \( y \)-coordinate remains the same. Therefore, the coordinates of point \( P^{\prime} \) after reflection are \( (-6, -5) \). To determine the quadrant for \( P^{\prime} \): - The \( x \)-coordinate is negative (-6), and the \( y \)-coordinate is also negative (-5). Points with negative \( x \) and negative \( y \) coordinates lie in the **Quadrant IV**. So the best answer is D. IV.
