To identify the lines of reflection that will flip the given coordinates onto themselves, we first note that the points provided suggest a square shape.
The points listed are:
- A (3, -4)
- B (3, 5)
- C (3, -2)
- D (3, -2)
However, it seems that point C is listed twice. Assuming you meant to have four unique points that form a square, let's clarify the reflection lines based on this shape.
Given that three of the points have an x-coordinate of 3, it appears this square is vertically oriented. Here are the possible lines of reflection:
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Vertical Line of Reflection: The vertical line of reflection would be the vertical line that bisects the square. This would be at \(x = 3\).
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Horizontal Line of Reflection: The horizontal line of reflection would be the horizontal line that bisects the square. This would be the average of the y-coordinates of the topmost and bottommost points.
Since the coordinates indicate:
- The lowest point A is at \(y = -4\).
- The highest point B is at \(y = 5\).
The midpoint for the y-coordinates is calculated as follows: \[ y_{\text{mid}} = \frac{-4 + 5}{2} = \frac{1}{2} \]
Therefore, the horizontal line of reflection is at \(y = \frac{1}{2}\).
So the completed statement would be: The lines of reflection are x = 3 and y = 1/2.
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