A left-parenthesis negative 3 comma negative 3 right-parenthesis right-arrow A prime is a glide reflection where the translation is left-parenthesis x comma y right-parenthesis right-arrow left-parenthesis x plus 5 comma y right-parenthesis, and the line of reflection is y = 1. What are the coordinates of A prime?
(1 point)
Responses
left-parenthesis 2 comma negative 3 right-parenthesis
Image with alt text: left-parenthesis 2 comma negative 3 right-parenthesis
left-parenthesis negative 3 comma 5 right-parenthesis
Image with alt text: left-parenthesis negative 3 comma 5 right-parenthesis
left-parenthesis 5 comma 1 right-parenthesis
Image with alt text: left-parenthesis 5 comma 1 right-parenthesis
left-parenthesis 2 comma 5 right-parenthesis
The coordinates of A prime are (2, -3).
To find the coordinates of A prime, we need to apply the given glide reflection transformation.
First, let's apply the translation component of the glide reflection, which is (x+5, y). The original coordinates of A are (-3, -3). Adding 5 to the x-coordinate gives:
(-3 + 5, -3) = (2, -3).
Next, let's consider the line of reflection, which is y = 1. We need to reflect the y-coordinate of A prime across this line, while keeping the x-coordinate the same. The y-coordinate of A prime is -3, which we need to reflect across y = 1, so:
y' = 2(1) - (-3)
y' = 2 + 3
y' = 5.
Putting it all together, the coordinates of A prime are (2, 5).