Geometry

Question Analysis:
This question involves applying a translation to a specific point of a triangle.
The main focus is on understanding how translations affect the coordinates of a figure.

Key Concept Explanation:
In geometry, a translation moves every point of a figure the same distance in a given direction.
The translation rule (x, y) → (x + a, y + b) means:
Add a to the x-coordinate
Add b to the y-coordinate
This keeps the shape and size the same—only the position changes.

Step-by-Step Solution:
We're given point B(4, 7) and a translation rule of (x + 3, y − 5).
Apply the rule:
New x-coordinate: 4 + 3 = 7
New y-coordinate: 7 − 5 = 2
So the new position of point B is (7, 2).

Common Mistakes:
Forgetting to apply both x and y changes
Adding instead of subtracting when negative movement i...