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 1/4
To find the coordinates after a dilation with a scale factor of 1/4, we multiply each coordinate by the scale factor.
For point (-0.5,2):
New x-coordinate = -0.5 * 1/4 = -0.125
New y-coordinate = 2 * 1/4 = 0.5
Therefore, (-0.5,2) becomes (-0.125,0.5).
For point (-0.5,-1):
New x-coordinate = -0.5 * 1/4 = -0.125
New y-coordinate = -1 * 1/4 = -0.25
Therefore, (-0.5,-1) becomes (-0.125,-0.25).
For point (1.5,2):
New x-coordinate = 1.5 * 1/4 = 0.375
New y-coordinate = 2 * 1/4 = 0.5
Therefore, (1.5,2) becomes (0.375,0.5).
For point (1.5,-1):
New x-coordinate = 1.5 * 1/4 = 0.375
New y-coordinate = -1 * 1/4 = -0.25
Therefore, (1.5,-1) becomes (0.375,-0.25).
So, the points after a dilation with a scale factor of 1/4 are:
(-0.5,2) becomes (-0.125,0.5)
(-0.5,-1) becomes (-0.125,-0.25)
(1.5,2) becomes (0.375,0.5)
(1.5,-1) becomes (0.375,-0.25)
To find the new coordinates of the points after a dilation with a scale factor of 1/4, we need to multiply the x and y coordinates of each point by the scale factor.
Let's start with the first point (-0.5, 2):
New x-coordinate = (-0.5) * (1/4) = -0.125
New y-coordinate = 2 * (1/4) = 0.5
So the new coordinates of the first point are approximately (-0.125, 0.5).
Next, let's move to the second point (-0.5, -1):
New x-coordinate = (-0.5) * (1/4) = -0.125
New y-coordinate = -1 * (1/4) = -0.25
So the new coordinates of the second point are approximately (-0.125, -0.25).
Moving on to the third point (1.5, 2):
New x-coordinate = (1.5) * (1/4) = 0.375
New y-coordinate = 2 * (1/4) = 0.5
So the new coordinates of the third point are approximately (0.375, 0.5).
Finally, let's calculate the fourth point (1.5, -1):
New x-coordinate = (1.5) * (1/4) = 0.375
New y-coordinate = -1 * (1/4) = -0.25
So the new coordinates of the fourth point are approximately (0.375, -0.25).
Therefore, after a dilation with a scale factor of 1/4, the new coordinates of the points are approximately:
1. (-0.125, 0.5)
2. (-0.125, -0.25)
3. (0.375, 0.5)
4. (0.375, -0.25)
To find the points after a dilation with a scale factor of 1/4, you need to multiply the x and y coordinates of each point by the scale factor.
Let's take the first point (-0.5, 2) as an example:
Dilation with scale factor of 1/4:
New x-coordinate = scale factor * original x-coordinate
= 1/4 * (-0.5)
= -0.125
New y-coordinate = scale factor * original y-coordinate
= 1/4 * 2
= 0.5
Therefore, the first point after the dilation is (-0.125, 0.5).
Similarly, we can find the coordinates for the other three points:
For the point (-0.5, -1):
New x-coordinate = scale factor * original x-coordinate
= 1/4 * (-0.5)
= -0.125
New y-coordinate = scale factor * original y-coordinate
= 1/4 * (-1)
= -0.25
The second point after the dilation is (-0.125, -0.25).
For the point (1.5, 2):
New x-coordinate = scale factor * original x-coordinate
= 1/4 * 1.5
= 0.375
New y-coordinate = scale factor * original y-coordinate
= 1/4 * 2
= 0.5
The third point after the dilation is (0.375, 0.5).
For the point (1.5, -1):
New x-coordinate = scale factor * original x-coordinate
= 1/4 * 1.5
= 0.375
New y-coordinate = scale factor * original y-coordinate
= 1/4 * (-1)
= -0.25
The fourth point after the dilation is (0.375, -0.25).
Therefore, after the dilation with the scale factor of 1/4, the four points become:
(-0.125, 0.5), (-0.125, -0.25), (0.375, 0.5), (0.375, -0.25).