Question

find a rule that translates △abc to △abc. enter the rule in the form (x + a, y + b).

Explanation:

Step1: Identify Coordinates of A and A'

Let's find coordinates of \( A \) and \( A' \). From the graph, \( A \) is at \( (1, 3) \) (assuming grid lines, let's confirm: \( A \) is 1 unit right of y-axis, 3 units up from x-axis). \( A' \) is at \( (-3, 6) \) (3 units left of y-axis, 6 units up).

Step2: Calculate \( a \) and \( b \)

For \( x \)-coordinate: \( x + a = -3 \), \( x = 1 \), so \( 1 + a = -3 \Rightarrow a = -4 \).
For \( y \)-coordinate: \( y + b = 6 \), \( y = 3 \), so \( 3 + b = 6 \Rightarrow b = 3 \).
Check with another point, say \( B \) and \( B' \). But with \( A \) we found \( a = -4 \), \( b = 3 \).

Answer:

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