Question

1. write a rule for the translation of $\triangle abc$ to $\triangle abc$.

Explanation:

Step1: Find coordinates of point A and A'

Assume grid units: Let A = (-3, 1), A' = (2, -4)

Step2: Calculate horizontal/vertical shifts

Horizontal shift: $2 - (-3) = 5$ (right 5 units). Vertical shift: $-4 - 1 = -5$ (down 5 units)

Step3: Verify with point B

Let B = (0, 3), B' = (5, -2). $5-0=5$, $-2-3=-5$ (matches)

Step4: Verify with point C

Let C = (1, 2), C' = (6, -3). $6-1=5$, $-3-2=-5$ (matches)

Answer:

$(x, y) \to (x + 5, y - 5)$