What you’ll learn
Perform and describe reflections.
Key idea
An axis reflection preserves the parallel coordinate and reverses the signed perpendicular one.
A non-axis point changes side at equal perpendicular distance; the parallel coordinate stays fixed.
Worked example
Enter the exact value or ordered values in the format requested below.
Reflect P=(-2,-2) across y-axis. Find its image.
- Reflecting (-2,-2) across y-axis preserves its parallel coordinate and negates its perpendicular coordinate.
- The image is (2,-2); the same reflection sends (2,-2) back to (-2,-2).
Answer: (2,-2)
Quick Check
Evaluate a worked attempt at perform and describe reflections, identify the first invalid step, and provide the correction.
Reflect P=(1,-1) across x-axis. Student: Step 1, x_image=1. Step 2, y_image=-1, since the point already lies on one side. Identify first invalid step and correct the image.