Question

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

Explanation:

Step1: Find coordinates of a point

Take point \( B \): original coordinates \( (-3, 1) \), new coordinates \( (1, 3) \).

Step2: Calculate x - change

\( 1 - (-3) = 4 \), so \( x \) increases by 4 (\( x + 4 \)).

Step3: Calculate y - change

\( 3 - 1 = 2 \), so \( y \) increases by 2 (\( y + 2 \)).

Answer:

\((x,y)\to(x + 4,y + 2)\)