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Question 13 (6 points):

ΔABC, with coordinates A(−8,4) , B(−5,8) , and C(−3,3) , is transformed by (x,y)→(x+4,y−6) to produce ΔA′B′C′ . ΔA′B′C′ is transformed by the rule (x,y)→(x+5,y−3) . Create a new rule that combines the two transformation rules. Use the function rules to find the coordinates of ΔA"B"C".

Answer 1

The two translations add: (4, −6) + (5, −3) = (9, −9). So the combined rule is (x,y) → (x+9, y−9).

Apply to each vertex:
- A'' = (−8+9, 4−9) = (1, −5)
- B'' = (−5+9, 8−9) = (4, −1)
- C'' = (−3+9, 3−9) = (6, −6)