The glide reflection Ry--x degree T <4,1> maps the P to (4,3). Find the coordinates of P. Please help I'm really confused.
Jhhh
To solve this problem, we need to understand what a glide reflection is and how it affects the coordinates of a point.
A glide reflection is a transformation that combines a reflection (R) and a translation (T) together. In this case, the glide reflection is denoted as Ry--x degree T <4,1>.
The "Ry--x degree" part indicates that the reflection is happening across the y-axis. The "--" represents the imaginary line created by the reflection.
The translation (T) is given as <4,1>, which means that after the reflection, the point is shifted 4 units in the positive x-direction and 1 unit in the positive y-direction.
Now, let's find the coordinates of P after the glide reflection.
1. Start with the coordinates of P, which we'll call (x, y).
2. Apply the reflection across the y-axis by negating the x-coordinate: (-x, y).
3. Apply the translation by adding the corresponding values to the x and y coordinates:
- For the x-coordinate, add 4 units: -x + 4.
- For the y-coordinate, add 1 unit: y + 1.
4. Equate the resulting coordinates with the given point after the glide reflection, which is (4, 3):
-x + 4 = 4, and y + 1 = 3.
5. Solve the equations:
-x = 4 - 4 = 0, and y = 3 - 1 = 2.
6. The x-coordinate is -x = -0 = 0, and the y-coordinate is y = 2.
7. Therefore, the coordinates of P are (0, 2).
So, the coordinates of P after the glide reflection are (0, 2).