Geometry

Question Analysis:
This question involves a sequence of two transformations:
A reflection over a vertical line
A translation (shift) in the coordinate plane
The main focus is understanding how to apply each transformation step-by-step and track coordinate changes.

Key Concept Explanation:
Reflection across x = c (vertical line):
x becomes 2c − x
y stays the same
Translation by (h, k):
x becomes x + h
y becomes y + k
(Here, h = −3 (left), k = +2 (up))

Step-by-Step Solution:
Step 1: Reflect A(4, −1) across x = 2
new x = 2 × 2 − 4 = 4 − 4 = 0
new y = −1
→ After reflection, A′ = (0, −1)
Step 2: Translate (0, −1) left 3 units and up 2 units
new x = 0 − 3 = −3
new y = −1 + 2 = 1
→ Final point = (−3, 1)

Common Mistakes:
Applying translation before refle...