Answer:
A'''(1,1), B'''(-2,-1) and C'''(-4,0).
Step-by-step explanation:
Triangle ABC has vertices with coordinates A(-6,-1), B(-3,-3) and C(-1,-2) (from given diagram).
1. Translation the triangle ABC 5 units to the right and 2 units up has a rule
(x,y)→(x+5,y+2).
Then the image triangle A'B'C' has vertices A'(-1,1), B'(2,-1) and C'(4,0).
2. Reflection the triangle A'B'C' across the line y=-x has a rule
(x,y)→(-y,-x).
Then the image triangle A"B"C" has vertices A"(-1,1) (this point lie on the line), B"(1,-2) and C"(0,-4).
3. Rotation the triangle A"B"C" counterclockwise about the origin by 270° has a rule
(x,y)→(y,-x).
Then the image triangle A'''B'''C''' has vertices A'''(1,1), B'''(-2,-1) and C'''(-4,0).
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