It looks like you've provided a series of transformations on points (A, B, C) in the coordinate plane, along with the final coordinates of those points after applying the transformations.
Here's a breakdown of the information you provided:
-
Initial Points and Transformations:
- Point A: (-8, 4) → A' (-4, -2)
- Point B: (-5, 8) → B' (-1, 2)
- Point C: (-3, 3) → C' (1, -3)
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Subsequent Transformations:
- Point A' → A'' (1, -5)
- Point B' → B'' (4, -1)
- Point C' → C'' (6, -6)
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Final Coordinates:
- A'' (1, -5)
- B'' (4, -1)
- C'' (6, -6)
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Composition Rule:
- (x, y) → (x + 9, y - 9)
Given that the composition rule is to add 9 to the x-coordinate and subtract 9 from the y-coordinate, we can apply this rule to the final points (A'', B'', and C''):
Applying the Composition Rule:
-
For A'' (1, -5):
- A''' = (1 + 9, -5 - 9) = (10, -14)
-
For B'' (4, -1):
- B''' = (4 + 9, -1 - 9) = (13, -10)
-
For C'' (6, -6):
- C''' = (6 + 9, -6 - 9) = (15, -15)
Final Coordinates after the rule:
- A''' = (10, -14)
- B''' = (13, -10)
- C''' = (15, -15)
You mentioned that the picture is located in Quadrant IV, which is correct since all of the coordinates for (A'', B'', C'') and their transformations fall in Quadrant IV where the x-coordinates are positive and the y-coordinates are negative.
If you have any further instructions or questions regarding these points or transformations, feel free to ask!