Question
Use the image to determine the line of reflection.
Graph of polygon ABCDE with point E at negative 3 comma 1. A second polygon A prime B prime C prime D prime E prime with E prime at negative 3 comma negative 3.
Reflection across the x-axis
Reflection across the y-axis
Reflection across y = −1
Reflection across x = −3
Graph of polygon ABCDE with point E at negative 3 comma 1. A second polygon A prime B prime C prime D prime E prime with E prime at negative 3 comma negative 3.
Reflection across the x-axis
Reflection across the y-axis
Reflection across y = −1
Reflection across x = −3
Answers
Answered by
GPT-4o mini
To determine the line of reflection between the original point E at coordinates (-3, 1) and the reflected point E' at coordinates (-3, -3), we can analyze the vertical position of these points.
The point E is at (-3, 1), and its reflection, E', is at (-3, -3). The y-coordinates of E and E' differ by 4 units (1 to -3). As E is above the x-axis and E' is below it, the line of reflection must be horizontal and located at the midpoint of the y-coordinates of E and E'.
To find the midpoint of the y-coordinates:
1. Take the average of the y-coordinates of E and E':
\[
\text{Midpoint} = \frac{1 + (-3)}{2} = \frac{-2}{2} = -1.
\]
Therefore, the line of reflection is the line \(y = -1\).
So, the correct answer is:
**Reflection across y = -1.**
The point E is at (-3, 1), and its reflection, E', is at (-3, -3). The y-coordinates of E and E' differ by 4 units (1 to -3). As E is above the x-axis and E' is below it, the line of reflection must be horizontal and located at the midpoint of the y-coordinates of E and E'.
To find the midpoint of the y-coordinates:
1. Take the average of the y-coordinates of E and E':
\[
\text{Midpoint} = \frac{1 + (-3)}{2} = \frac{-2}{2} = -1.
\]
Therefore, the line of reflection is the line \(y = -1\).
So, the correct answer is:
**Reflection across y = -1.**