Answer :
Answer:
Step-by-step explanation:To solve the problem, follow these steps:
1. **Reflect Shape A in the y-axis:**
Let's assume Shape A has the following coordinates:
\[
A: (x_1, y_1), (x_2, y_2), (x_3, y_3), \ldots
\]
When reflecting these points in the y-axis, the x-coordinates change sign while the y-coordinates remain the same:
\[
B: (-x_1, y_1), (-x_2, y_2), (-x_3, y_3), \ldots
\]
2. **Translate Shape B by the vector (2, -5):**
Translation by the vector (2, -5) means adding 2 to the x-coordinates and subtracting 5 from the y-coordinates of each point of Shape B:
\[
C: (-x_1 + 2, y_1 - 5), (-x_2 + 2, y_2 - 5), (-x_3 + 2, y_3 - 5), \ldots
\]
Let's apply these steps to a concrete example. Assume Shape A has the coordinates:
\[
A: (1, 2), (3, 4), (5, 6)
\]
**Reflect Shape A in the y-axis to get Shape B:**
\[
B: (-1, 2), (-3, 4), (-5, 6)
\]
**Translate Shape B by the vector (2, -5) to get the final coordinates:**
\[
C: (-1 + 2, 2 - 5), (-3 + 2, 4 - 5), (-5 + 2, 6 - 5)
\]
\[
C: (1, -3), (-1, -1), (-3, 1)
\]
Thus, the new coordinates after reflecting Shape A in the y-axis and translating by the vector (2, -5) are:
\[
C: (1, -3), (-1, -1), (-3, 1)
\]
