Geometry

Question Analysis:
This question requires applying a sequence of three rigid motions (isometries) to a single point.
The main focus is determining how the point moves step by step through rotation, reflection, and translation.

Key Concept Explanation:
90° Counterclockwise Rotation about the Origin: Changes (x, y) to (–y, x)
Reflection over the x-axis: Keeps x the same, changes the sign of y
Translation: Add or subtract units to x and y based on the direction of movement

Step-by-Step Solution:
Start with point A(–1, –3)
Rotate 90° counterclockwise around origin
New coordinates: (3, –1)
Reflect over the x-axis
Reflect y → (3, 1)
Translate 4 units right and 1 unit up
x: 3 + 4 = 7
y: 1 + 1 = 2
✅ Final coordinates: (7, 2)

Option Analysis:
A. (7, 2) → ✅ Correct
B. (3, 1) → Translation not applied
C. (–3, –1) → Possibly from misrotating or reversing the x sign
D. (5, –2) → Common trap from wrong translation direction

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