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'
A.(2,-3)
B.(-3,5)
C.(5,1)
D.(2,5)
Well, A is having quite the reflection party, isn't it? Let's break it down, shall we?
First, let's apply the translation. A starts at (-3,3) and moves 5 units to the right, which gives us (2,3). So far, so good!
Next, let's consider the line of reflection, y=1. This means that the y-coordinate gets reflected across this line. In other words, it flips the sign. So, the y-coordinate of (2,3) becomes (2,-3).
So, the coordinates of A' are (2,-3).
Therefore, the correct answer is A. (2,-3). Keep the reflection party going!
To find the coordinates of A', we need to apply the glide reflection transformation to the point A(-3,3).
1. Translate the point A by the given translation vector (x+5, y):
New x-coordinate = -3 + 5 = 2
New y-coordinate = 3
2. Reflect the translated point across the line of reflection y = 1:
The line of reflection is y = 1, and the new y-coordinate is currently 3.
The difference between the given line of reflection (y = 1) and the new y-coordinate (3) is 3 - 1 = 2.
Subtracting this difference from the new y-coordinate, we get: 3 - 2 = 1.
Therefore, the coordinates of A' are (2, 1).
The correct answer is A. (2, -3).
To find the coordinates of A' which is the image of point A under the glide reflection transformation, we can follow these steps:
1. Start with the given point A(-3,3).
2. Apply the translation component of the glide reflection. The translation vector is (x,y) -> (x+5,y). So, to translate A by this vector, we add 5 to the x-coordinate and leave the y-coordinate unchanged.
New coordinates after translation: A' = (-3 + 5, 3) = (2, 3).
3. Now, we need to reflect A' over the line of reflection y=1. To do this, we can calculate the distance between A' and the line y=1, and then reflect A' by that same distance on the other side of the line.
The distance between A' and the line y=1 is the vertical distance between the y-coordinate of A' and the line y=1. Since the y-coordinate of A' is 3, the distance is 3 - 1 = 2.
4. Reflect A' over the line y=1 by moving it 2 units below the line.
New coordinates after reflection: A'' = (2, 1).
So, the coordinates of A' after the glide reflection are (2, 1).
Therefore, the correct answer is option C. (5,1).