To find the glide reflection image of the blue triangle given the translation and line of reflection, you can follow these steps:
1. **Translation**: The translation specified is by the vector (7, 7). This means that every point of the triangle will be moved 7 units to the right and 7 units up. If the original points of the triangle are A(x1, y1), B(x2, y2), and C(x3, y3), the new points after translation will be:
- A'(x1 + 7, y1 + 7)
- B'(x2 + 7, y2 + 7)
- C'(x3 + 7, y3 + 7)
2. **Reflection**: The line of reflection is given as x = 1. To reflect each of the translated points across this line, we need to determine the distance of each point to the line and then place the reflected point on the opposite side of the line at the same distance:
- For each point A’, B’, and C’, calculate the horizontal distance from the line x = 1.
- The reflected point A” will be at: A”(1 – (A’.x – 1), A’.y), and similarly for B” and C”.
3. **Final Points**: After performing the reflection for each of the translated points, you will have the final positions of A”, B”, and C”, which represent the glide reflection image of the original triangle.
By following these steps meticulously, you ensure accurate representation of the glide reflection in your geometric transformations.