Question

identify the rule for the transformation shown in the figure that translates triangle abc into triangle abc. \\(\circ\\) \\((x, y) \to (x - 4, y - 2)\\) \\(\circ\\) \\((x, y) \to (x + 4, y - 2)\\) \\(\circ\\) \\((x, y) \to (x - 4, y + 2)\\) \\(\circ\\) \\((x, y) \to (x + 4, y + 2)\\)

Explanation:

Step1: Find coordinates of a point

Take point \( B \) from triangle \( ABC \). From the graph, \( B \) has coordinates \( (-3, 1) \). Point \( B' \) in triangle \( A'B'C' \) has coordinates \( (1, 3) \).

Step2: Calculate horizontal and vertical changes

Horizontal change: \( 1 - (-3) = 4 \), so \( x \)-coordinate changes by \( +4 \). Vertical change: \( 3 - 1 = 2 \), so \( y \)-coordinate changes by \( +2 \). Thus, the transformation rule is \( (x, y) \to (x + 4, y + 2) \).

Answer:

\( (x, y) \to (x + 4, y + 2) \) (the last option)