Geometry

Question Analysis:
This question involves reflecting an entire triangle across a vertical line.
The main focus is on applying the reflection rule to each vertex individually and understanding that only the x-coordinate changes in a vertical reflection.

Key Concept Explanation:
For a vertical line reflection over x = c:
The y-coordinate stays the same.
The x-coordinate becomes 2c − (original x).
Reflect each vertex one at a time, and then write down the new triangle's coordinates.

Step-by-Step Solution:
We reflect each point across the line x = 5.
Point A(2, 1):
New x = 2 × 5 − 2 = 10 − 2 = 8
So A′ = (8, 1)
Point B(4, 3):
New x = 2 × 5 − 4 = 10 − 4 = 6
So B′ = (6, 3)
Point C(6, 1):
New x = 2 × 5 − 6 = 10 − 6 = 4
So C′ = (4, 1)
Image triangle A′B′C′ has coordinates:
A′(8, 1), B′(6, 3), C′(4, 1)

Common Mistakes:
Forgetting to apply the formula 2c −...