Final answer:
After applying the translation (x, y) → (x - 7, y + 3), the new coordinates for points A, B, and C are A' (-6, 4), B' (1, 6), and C' (-1, 8), respectively.
Step-by-step explanation:
The student's question involves a translation of points in the coordinate plane, which is a topic in Mathematics. Specifically, the student is asking about the result of a translation transformation applied to points A (1,1), B (8,3), and C (6,5) using the rule (x, y) → (x - 7, y + 3).
To find the new coordinates after the translation:
- For point A (1,1), subtract 7 from the x-coordinate and add 3 to the y-coordinate: A' (1 - 7, 1 + 3) = A' (-6, 4).
- For point B (8,3), apply the same rule: B' (8 - 7, 3 + 3) = B' (1, 6).
- For point C (6,5), again apply the rule: C' (6 - 7, 5 + 3) = C' (-1, 8).
As a result, the new coordinates are:
- Point A' is at (-6, 4)
- Point B' is at (1, 6)
- Point C' is at (-1, 8)