Question

if the point g(-4, 6) was moved horizontally 4 units to the left, which of the following is the correct mapping to define the translation?
○ (x, y) → (x, y + 4)
○ (x, y) → (x + 4, y)
○ (x, y) → (x, y − 4)
○ (x, y) → (x − 4, y)

Explanation:

Step1: Recall horizontal translation rules

In coordinate geometry, a horizontal translation (left or right) affects the \( x \)-coordinate. Moving left decreases the \( x \)-coordinate, and moving right increases it. A vertical translation (up or down) affects the \( y \)-coordinate.

Step2: Analyze the given movement

The point \( G(-4, 6) \) is moved horizontally 4 units to the left. For a horizontal left - shift of \( a \) units, the transformation rule is \( (x,y)\to(x - a,y) \). Here, \( a = 4 \), so the rule should be \( (x,y)\to(x-4,y) \). Let's also check the other options:

• Option \( (x,y)\to(x,y + 4) \): This is a vertical shift up by 4 units, not horizontal.
• Option \( (x,y)\to(x + 4,y) \): This is a horizontal shift right by 4 units, not left.
• Option \( (x,y)\to(x,y - 4) \): This is a vertical shift down by 4 units, not horizontal.

Answer:

\( (x, y) \to (x - 4, y) \)