Use the image to determine the line of reflection.

Question

Graph of polygon ABCDE with point E at negative 6 comma 3. A second polygon A prime B prime C prime D prime E prime with E prime at negative 6 comma negative 1.
Reflection across x = −6
Reflection across y = 1
Reflection across the x-axis
Reflection across the y-axis

Answer 1

To determine the line of reflection between polygon ABCDE and its reflection A'B'C'D'E', we can analyze the coordinates of points E and E':

• Point E is at \((-6, 3)\).
• Point \(E'\) is at \((-6, -1)\).

To find the line of reflection, we can observe that the x-coordinates of both points are the same, \(-6\). The difference in the y-coordinates is \(3 - (-1) = 3 + 1 = 4\). The line of reflection would be at the midpoint of the y-coordinates of points E and \(E'\).

Calculating the midpoint:

• The midpoint y-coordinate is \(\frac{3 + (-1)}{2} = \frac{3 - 1}{2} = \frac{2}{2} = 1\).

Since the x-coordinates are identical, the line of reflection must be vertical along the x-coordinate \(-6\).

So the line of reflection is therefore: Reflection across the line \(y = 1\).

None of the other options (the x-axis, y-axis, or the line \(x = -6\)) correctly describe the line of reflection for the points given.