What are the points (-0.5,2), (-0.5,-1), (1.5,2), and (1.5,-1) after a dilation with the scale factor of 1/2?
To dilate a point by a scale factor of 1/2, we multiply both the x-coordinate and the y-coordinate of the original point by 1/2.
For the point (-0.5, 2), multiplying the x-coordinate and the y-coordinate by 1/2 yields:
(-0.5 * 1/2, 2 * 1/2) = (-0.25, 1)
For the point (-0.5, -1), multiplying the x-coordinate and the y-coordinate by 1/2 yields:
(-0.5 * 1/2, -1 * 1/2) = (-0.25, -0.5)
For the point (1.5, 2), multiplying the x-coordinate and the y-coordinate by 1/2 yields:
(1.5 * 1/2, 2 * 1/2) = (0.75, 1)
For the point (1.5, -1), multiplying the x-coordinate and the y-coordinate by 1/2 yields:
(1.5 * 1/2, -1 * 1/2) = (0.75, -0.5)
Therefore, after a dilation with a scale factor of 1/2, the new coordinates are:
(-0.25, 1), (-0.25, -0.5), (0.75, 1), and (0.75, -0.5)
To find the points after a dilation with a scale factor of 1/2, we can multiply the coordinates of each point by the scale factor.
Let's start with the point (-0.5, 2):
- Multiply the x-coordinate (-0.5) by the scale factor (1/2): (-0.5) * (1/2) = -0.25
- Multiply the y-coordinate (2) by the scale factor (1/2): 2 * (1/2) = 1
So, after the dilation, the point (-0.5, 2) becomes (-0.25, 1).
Next, let's find the new coordinates for the point (-0.5, -1):
- Multiply the x-coordinate (-0.5) by the scale factor (1/2): (-0.5) * (1/2) = -0.25
- Multiply the y-coordinate (-1) by the scale factor (1/2): -1 * (1/2) = -0.5
Therefore, after the dilation, the point (-0.5, -1) becomes (-0.25, -0.5).
Similarly, for the point (1.5, 2):
- Multiply the x-coordinate (1.5) by the scale factor (1/2): (1.5) * (1/2) = 0.75
- Multiply the y-coordinate (2) by the scale factor (1/2): 2 * (1/2) = 1
After the dilation, the point (1.5, 2) becomes (0.75, 1).
Lastly, let's find the new coordinates for the point (1.5, -1):
- Multiply the x-coordinate (1.5) by the scale factor (1/2): (1.5) * (1/2) = 0.75
- Multiply the y-coordinate (-1) by the scale factor (1/2): -1 * (1/2) = -0.5
Therefore, after the dilation, the point (1.5, -1) becomes (0.75, -0.5).
To summarize, the points (-0.5, 2), (-0.5, -1), (1.5, 2), and (1.5, -1) after a dilation with a scale factor of 1/2 are (-0.25, 1), (-0.25, -0.5), (0.75, 1), and (0.75, -0.5) respectively.
To find the coordinates of the points after a dilation with a scale factor of 1/2, you need to multiply the x-coordinates and y-coordinates by the scale factor.
Let's take the first point (-0.5, 2) as an example.
1. Multiply the x-coordinate (-0.5) by the scale factor (1/2):
(-0.5) * (1/2) = -0.25
2. Multiply the y-coordinate (2) by the scale factor (1/2):
2 * (1/2) = 1
So, after the dilation, the first point becomes (-0.25, 1).
You can repeat this process for the remaining points:
For the second point (-0.5, -1):
1. Multiply the x-coordinate (-0.5) by the scale factor (1/2):
(-0.5) * (1/2) = -0.25
2. Multiply the y-coordinate (-1) by the scale factor (1/2):
-1 * (1/2) = -0.5
After the dilation, the second point becomes (-0.25, -0.5).
For the third point (1.5, 2):
1. Multiply the x-coordinate (1.5) by the scale factor (1/2):
1.5 * (1/2) = 0.75
2. Multiply the y-coordinate (2) by the scale factor (1/2):
2 * (1/2) = 1
After the dilation, the third point becomes (0.75, 1).
And for the fourth point (1.5, -1):
1. Multiply the x-coordinate (1.5) by the scale factor (1/2):
1.5 * (1/2) = 0.75
2. Multiply the y-coordinate (-1) by the scale factor (1/2):
-1 * (1/2) = -0.5
After the dilation, the fourth point becomes (0.75, -0.5).
So, the new coordinates after the dilation with a scale factor of 1/2 are:
(-0.25, 1), (-0.25, -0.5), (0.75, 1), and (0.75, -0.5).