Geometry

Question Analysis:
This question involves two transformations in sequence:
A reflection across a horizontal line
A translation (slide) involving horizontal and vertical shifts
The main focus is understanding how to apply multiple transformations step-by-step to a point.

Key Concept Explanation:
Reflection across y = a: Flip the y-coordinate over line y = a
→ New y = a + (a − original y) = 2a − original y
Translation (x + a, y + b):
→ Shift x by a, y by b
→ Right = +, Left = −, Up = +, Down = −

Step-by-Step Solution:
Original point F: (4, 1)
Step 1 — Reflect across y = 3
Keep x = 4
y changes: 3 is midpoint between 1 and the image
Use formula: 2 × 3 − 1 = 5
Reflected point = (4, 5)
Step 2 — Translate (Right 2, Down 1)
Add 2 to x: 4 + 2 = 6
Subtract 1 from y: 5 − 1 = 4
Final image = (6, 4)

Common Mistakes:
R...