To find the lines of reflection that will flip the rectangle onto itself, we need to examine the coordinates of the points.
The rectangle has the following vertices:
- A(-4, 3)
- B(5, 3)
- C(5, -2)
- D(-4, -2)
1. Line of reflection for symmetry across the vertical axis (x-axis):
The x-coordinates of points A and D are both -4, and the x-coordinates of points B and C are both 5. The midpoints between these paired points can help us find a vertical line of reflection.
The midpoint of line segment AB is:
- Midpoint = ((-4 + 5)/2, (3 + 3)/2) = (0.5, 3)
The midpoint of line segment CD is:
- Midpoint = ((-4 + 5)/2, (-2 + -2)/2) = (0.5, -2)
The x-coordinate halfway between -4 and 5 is: \[ \text{Midpoint in the x-direction} = \frac{-4 + 5}{2} = \frac{1}{2} = 0.5 \]
2. Line of reflection for symmetry across the horizontal axis (y-axis):
Looking at the y-coordinates, we can see that:
- Points A and B have the y-coordinate of 3.
- Points C and D have the y-coordinate of -2. The midpoint for the vertical lines can be calculated as: \[ \text{Midpoint in the y-direction} = \frac{3 + (-2)}{2} = \frac{1}{2} = 0.5 \]
Thus, based on analysis:
- The vertical line of reflection: \( x = 0.5 \)
- The horizontal line of reflection: \( y = 0.5 \)
To summarize:
- The lines of reflection are:
- x = 0.5
- y = 0.5
Hence, the final answers are:
- The lines of reflection are \( x=0.5 \) and \( y=0.5 \).