Question

use the figure to identify the correct rule for the translation.
$(x,y) \to (x - 3, y + 4)$
$(x,y) \to (x + 3, y - 4)$
$(x,y) \to (x - 4, y + 3)$
$(x,y) \to (x + 4, y - 3)$

Explanation:

Step1: Identify coordinates of a point

Take point \( A \) and \( A' \). From the graph, \( A \) is at \( (4, -1) \) and \( A' \) is at \( (1, 3) \).

Step2: Calculate horizontal and vertical changes

Horizontal change: \( 1 - 4 = -3 \) (so \( x \) changes by \( -3 \), i.e., \( x - 3 \)).
Vertical change: \( 3 - (-1) = 4 \) (so \( y \) changes by \( +4 \), i.e., \( y + 4 \)).

Step3: Verify with another point

Take \( C \) at \( (1, -2) \) and \( C' \) at \( (-2, 2) \). Horizontal: \( -2 - 1 = -3 \), Vertical: \( 2 - (-2) = 4 \). Matches \( (x, y) \to (x - 3, y + 4) \).

Answer:

\( (x, y) \to (x - 3, y + 4) \)