A(-3,-3)-->A'is a glide reflection where the translation is (x,y)-->(x+5,y, and the line of reflection is y = 1. What are the coordinates of A'?
first transformation:
(x,y) ---> (x+5,y)
(-3,-3) ----> (2,-3)
second transformation:
reflection in y = 1
(x,y) ---> (x, 2-y)
(2,-3) ----> (2, 5)
A' is (2,5)
To find the coordinates of A' in the glide reflection, we can follow these steps:
1. Start with point A(-3, -3).
2. Apply the translation (x, y) → (x + 5, y), which means adding 5 to the x-coordinate of A but leaving the y-coordinate unchanged. So, the translated point A' is (-3 + 5, -3) → (2, -3).
3. Apply the reflection over the line y = 1. In a reflection, points on the line remain fixed, while points above the line move below it, and points below the line move above it.
- Since point A' has a y-coordinate of -3, which is below y = 1, it will move above the line after reflection.
- The distance between A' and the line y = 1 is 2 units (-3 to 1). After reflection, the distance should remain the same. Therefore, the new y-coordinate will be obtained by subtracting 2 units from 1, due to the distance from A' to the line y = 1: 1 - 2 = -1.
- The new coordinates of A' after reflection will be (2, -1).
Therefore, the coordinates of A' in the glide reflection are (2, -1).
To find the coordinates of A' in the glide reflection, we need to perform two transformations: a translation and a reflection.
Let's start with the translation. We are given that the translation is (x, y) --> (x + 5, y). To apply this translation to point A(-3, -3), we add 5 to the x-coordinate and leave the y-coordinate unchanged.
Adding 5 to -3, we get -3 + 5 = 2. So, the coordinates of the image of A after the translation are (2, -3).
Now, we need to apply the reflection. The line of reflection is y = 1. To reflect a point over this line, we keep the x-coordinate the same and change the sign of the y-coordinate.
So, for point (2, -3), the reflected point A' will have the same x-coordinate but the opposite sign for the y-coordinate.
Therefore, the coordinates of A' in the glide reflection are (2, -(-3)) or simply (2, 3).