Final answer:
The question involves translating a set of points horizontally on a coordinate plane, both positively and negatively. By adding or subtracting from the x-coordinates accordingly, we find the new positions of the points after translation. The correct answer is A: A' (10, 4), B' (11, 6), C' (13, 1), D' (-7, 2), E' (-6, 5), F' (-1, 5), G' (-2, 2).
Step-by-step explanation:
The question involves the translation of points in a two-dimensional plane, which is a concept from mathematics. The original coordinates (A', B', C') are each translated 4 units horizontally, which means adding 4 to the x-coordinate of each point.
Similarly, the second set of points (D, E, F, G) are translated -7 units horizontally, which means subtracting 7 from the x-coordinate of each point. The new coordinates will give us the translated points. Here's how to calculate them:
- A' (6,4) becomes A' (6+4, 4) = A' (10, 4)
- B' (7,6) becomes B' (7+4, 6) = B' (11, 6)
- C' (9,1) becomes C' (9+4, 1) = C' (13, 1)
- D (0,2) becomes D' (0-7, 2) = D' (-7, 2)
- E (1,5) becomes E' (1-7, 5) = E' (-6, 5)
- F (6,5) becomes F' (6-7, 5) = F' (-1, 5)
- G (5,2) becomes G' (5-7, 2) = G' (-2, 2)
Therefore, the correct set of coordinates after the translations is A' (10, 4), B' (11, 6), C' (13, 1), D' (-7, 2), E' (-6, 5), F' (-1, 5), G' (-2, 2), which corresponds to option A.