To determine the lines of reflection that will flip the given quadrilateral ABCD onto itself, we first need to identify the midpoints between pairs of corresponding vertices. This will help us figure out the lines of reflection.
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Identify Points:
- A = (-4, 3)
- B = (5, 3)
- C = (5, -2)
- D = (-4, -2)
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Find Midpoints: The midpoints between pairs of vertices (A and C, B and D) will help in finding the lines of reflection.
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Midpoint of AC: \[ M_{AC} = \left( \frac{-4 + 5}{2}, \frac{3 + (-2)}{2} \right) = \left( \frac{1}{2}, \frac{1}{2} \right) \]
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Midpoint of BD: \[ M_{BD} = \left( \frac{5 + (-4)}{2}, \frac{3 + (-2)}{2} \right) = \left( \frac{1}{2}, \frac{1}{2} \right) \]
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Both midpoints are the same indicating symmetry along diagonals.
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Determine Lines of Reflection: The lines that will reflect ABCD onto itself can be:
Vertical line of reflection (x-axis): \[ x = \frac{1}{2} \]
Horizontal line of reflection (y-axis): \[ y = 0.5 \]
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Equation Summary: Thus, the lines of reflection that will flip the quadrilateral ABCD onto itself are:
\[ X = \frac{1}{2}, Y = \frac{1}{2} \]
If you are looking for integer values or standard forms, it may help to represent them as:
\[ \text{Horizontal Line: } Y = 0 \] \[ \text{Vertical Line: } X = 0 \] or \[ X = 0,\ Y = 0 \]
In this case, the answer to enter would be: \[ X = 0.5 \quad Y = 0.5 \] or you could use simple integers if requested.