Hello! I'd be happy to help you with this question.
To find the endpoints of the image of PQ after the composition of the given translations, let's first apply the translations step by step to the initial endpoints of PQ.
Given translations:
1. Translation: (x, y) → (x-1, y+6)
2. Translation: (x, y) → (2, y+3)
Let's apply these translations to the endpoints of PQ:
- For point P(5, -2):
1. Translation 1: (5-1, -2+6) = (4, 4)
2. Translation 2: (2, 4+3) = (2, 7)
So, the image of point P(5, -2) is P"(2, 7).
- For point Q(-1, 4):
1. Translation 1: (-1-1, 4+6) = (-2, 10)
2. Translation 2: (2, 10+3) = (2, 13)
Therefore, the image of point Q(-1, 4) is Q"(2, 13).
In conclusion, the endpoints of the image of PQ after the composition of the given translations are:
- P" at (2, 7)
- Q" at (2, 13)
I hope this explanation helps you understand how the endpoints were determined. Let me know if you have any further questions or need clarification.
