What are the points (-1,2), (-1,-1), (2,2), and (2,-1) after a dilation with the scale factor of 2?
A dilation with a scale factor of 2 means that every coordinate will be multiplied by 2.
For the point (-1,2), the x-coordinate becomes -1 * 2 = -2 and the y-coordinate becomes 2 * 2 = 4. Thus, after the dilation, the point (-1,2) becomes (-2,4).
For the point (-1,-1), the x-coordinate becomes -1 * 2 = -2 and the y-coordinate becomes -1 * 2 = -2. Thus, after the dilation, the point (-1,-1) remains the same, (-1,-1).
For the point (2,2), the x-coordinate becomes 2 * 2 = 4 and the y-coordinate becomes 2 * 2 = 4. Thus, after the dilation, the point (2,2) becomes (4,4).
For the point (2,-1), the x-coordinate becomes 2 * 2 = 4 and the y-coordinate becomes -1 * 2 = -2. Thus, after the dilation, the point (2,-1) becomes (4,-2).
Therefore, after a dilation with a scale factor of 2, the points (-1,2), (-1,-1), (2,2), and (2,-1) become (-2,4), (-1,-1), (4,4), and (4,-2) respectively.
To perform a dilation with a scale factor of 2, you multiply the coordinates of each point by 2.
Let's find the coordinates after dilation for each given point:
1. Point (-1,2):
- Multiply the x-coordinate (-1) by 2: -1 * 2 = -2
- Multiply the y-coordinate (2) by 2: 2 * 2 = 4
The new coordinates after dilation are (-2, 4).
2. Point (-1,-1):
- Multiply the x-coordinate (-1) by 2: -1 * 2 = -2
- Multiply the y-coordinate (-1) by 2: -1 * 2 = -2
The new coordinates after dilation are (-2, -2).
3. Point (2,2):
- Multiply the x-coordinate (2) by 2: 2 * 2 = 4
- Multiply the y-coordinate (2) by 2: 2 * 2 = 4
The new coordinates after dilation are (4, 4).
4. Point (2,-1):
- Multiply the x-coordinate (2) by 2: 2 * 2 = 4
- Multiply the y-coordinate (-1) by 2: -1 * 2 = -2
The new coordinates after dilation are (4, -2).
Therefore, the points after a dilation with a scale factor of 2 are:
(-2, 4), (-2, -2), (4, 4), and (4, -2).
To find the points after a dilation with a scale factor of 2, we need to multiply the coordinates of each point by the scale factor.
Let's start with the first point (-1,2):
- Multiply the x-coordinate (-1) by the scale factor 2: -1 * 2 = -2
- Multiply the y-coordinate (2) by the scale factor 2: 2 * 2 = 4
So, the new coordinates for the point (-1,2) after the dilation with a scale factor of 2 are (-2, 4).
Now let's move on to the second point (-1,-1):
- Multiply the x-coordinate (-1) by the scale factor 2: -1 * 2 = -2
- Multiply the y-coordinate (-1) by the scale factor 2: -1 * 2 = -2
Therefore, the new coordinates for the point (-1,-1) after the dilation with a scale factor of 2 are (-2, -2).
Now let's find the new coordinates for the third point (2,2):
- Multiply the x-coordinate (2) by the scale factor 2: 2 * 2 = 4
- Multiply the y-coordinate (2) by the scale factor 2: 2 * 2 = 4
So, the new coordinates for the point (2,2) after the dilation with a scale factor of 2 are (4, 4).
Lastly, let's determine the new coordinates for the fourth point (2,-1):
- Multiply the x-coordinate (2) by the scale factor 2: 2 * 2 = 4
- Multiply the y-coordinate (-1) by the scale factor 2: -1 * 2 = -2
Hence, the new coordinates for the point (2,-1) after the dilation with a scale factor of 2 are (4, -2).
To summarize, after the dilation with a scale factor of 2, the new coordinates for the given points are:
(-1,2) → (-2, 4)
(-1,-1) → (-2, -2)
(2,2) → (4, 4)
(2,-1) → (4, -2)