. Point A (-3,-3) to A’ is a glide reflection where the translation is (x+2, y) and the line of reflection is y=1? What are the new coordinates?
To find the new coordinates of point A after a glide reflection, we need to first apply the translation and then reflect the translated point across the line of reflection.
Applying the translation (x+2, y) to point A (-3,-3), we get:
A' = (-3+2, -3) = (-1, -3)
Now, we need to reflect point A' across the line of reflection y=1. To do this, we can find the distance between point A' and the line of reflection, and then move the point the same distance on the other side of the line.
The distance between point A' and the line y=1 is 1 unit (since the y-coordinate of A' is already 1 unit below the line). So, we can move the point 1 unit above the line to get the reflected point:
A'' = (-1, -3+1) = (-1, -2)
Therefore, the new coordinates of point A after the glide reflection are (-1, -2).
To find the new coordinates of point A (-3, -3) under the glide reflection with the given translation and the line of reflection, we follow these steps:
1. First, apply the translation by adding 2 to the x-coordinate:
x' = x + 2
= -3 + 2
= -1
The new x-coordinate is -1.
2. Next, the y-coordinate remains the same under the translation:
y' = y
= -3
The new y-coordinate is -3.
3. Finally, we need to reflect the new point in the line y = 1.
Since the y-coordinate of the line of reflection is fixed at 1, we need to find the new y-coordinate by calculating the difference between the line of reflection and the current y-coordinate:
y' = 2 * (line of reflection) - y
= 2 * 1 - (-3)
= 2 + 3
= 5
The new y-coordinate is 5.
Therefore, the new coordinates of point A' are (-1, 5).
To find the new coordinates after a glide reflection, we need to apply both a translation and a reflection to the original coordinates.
The translation given is (x+2, y), which means that every point's x-coordinate is increased by 2 units while the y-coordinate remains the same.
The line of reflection is y=1, which means that every point is reflected across this line.
Let's start with the initial point A (-3, -3).
First, apply the translation by adding 2 to the x-coordinate and leaving the y-coordinate unchanged:
New coordinates after translation = (x + 2, y) = (-3 + 2, -3) = (-1, -3).
Next, apply the reflection by finding the distance between the line of reflection y=1 and the y-coordinate of the translated point, and then adding or subtracting this distance from the line of reflection. Since the y-coordinate of the translated point is -3, the distance is 1 - (-3) = 4 units.
Since the point is reflected below the line of reflection, we subtract the distance from the line.
New coordinates after reflection = (-1, 1 - 4) = (-1, -3).
Therefore, the new coordinates after the glide reflection are A'(-1,-3).