To find the lines of reflection that will flip the figure formed by the given points onto itself, we need to identify the midpoints of the horizontal and vertical segments that run through these points.
Given the points:
- Point A: (-4, 3)
- Point B: (5, 3)
- Point C: (5, -2)
- Point D: (-4, -2)
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Horizontal Line of Reflection: The y-coordinates of points A and B are both 3, and the y-coordinates of points C and D are both -2. To find the horizontal line of reflection, we can take the average of the y-coordinates from the top set (A and B) and the bottom set (C and D):
\[ \text{Midpoint y-coordinate} = \frac{3 + (-2)}{2} = \frac{1}{2} \]
Therefore, the line of reflection is: \[ y = \frac{1}{2} \]
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Vertical Line of Reflection: The x-coordinates of points A and D are both -4, and the x-coordinates of points B and C are both 5. To find the vertical line of reflection, we can take the average of the x-coordinates from the left set (A and D) and the right set (B and C):
\[ \text{Midpoint x-coordinate} = \frac{-4 + 5}{2} = \frac{1}{2} \]
Therefore, the line of reflection is: \[ x = \frac{1}{2} \]
In conclusion, the equations for the lines of reflection that will flip the given figure onto itself are:
- The vertical line: \( x = \frac{1}{2} \)
- The horizontal line: \( y = \frac{1}{2} \)
Thus, you can complete the statement as:
The lines of reflection are \( x = \frac{1}{2} \) and \( y = \frac{1}{2} \).
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