Angle DEF contains the points D(-5,5), E(-10,-5), and F (0,-5). Describe the effect of the dilation of the angle with a scale factor of 1/5 and a center point of dilation at the origin (0,0).
The dilation of the angle DEF with a scale factor of 1/5 and a center point of dilation at the origin (0,0) means that each point D, E, and F will be moved closer to the origin by a factor of 1/5.
To find the new coordinates of D after the dilation, we multiply each coordinate of D by 1/5:
-5 * 1/5 = -1
5 * 1/5 = 1
So the new coordinates of D after dilation are D'(-1,1).
Similarly, for point E:
-10 * 1/5 = -2
-5 * 1/5 = -1
So the new coordinates of E after dilation are E'(-2,-1).
And for point F:
0 * 1/5 = 0
-5 * 1/5 = -1
So the new coordinates of F after dilation are F'(0,-1).
Therefore, after the dilation with a scale factor of 1/5 and a center at the origin, the new angle DE'F' would be formed with new points D'(-1,1), E'(-2,-1), and F'(0,-1).
To describe the effect of the dilation on angle DEF with a scale factor of 1/5 and a center point at the origin (0,0), we need to consider how each point in the angle is affected.
1. Point D(-5,5):
- After the dilation with a scale factor of 1/5, the new coordinates of D can be found by multiplying the original coordinates of D by the scale factor:
- New x-coordinate of D = -5 * (1/5) = -1
- New y-coordinate of D = 5 * (1/5) = 1
- Therefore, the new coordinates of D become (-1, 1).
2. Point E(-10,-5):
- After the dilation with a scale factor of 1/5, the new coordinates of E can be found by multiplying the original coordinates of E by the scale factor:
- New x-coordinate of E = -10 * (1/5) = -2
- New y-coordinate of E = -5 * (1/5) = -1
- Therefore, the new coordinates of E become (-2, -1).
3. Point F(0,-5):
- After the dilation with a scale factor of 1/5, the new coordinates of F can be found by multiplying the original coordinates of F by the scale factor:
- New x-coordinate of F = 0 * (1/5) = 0
- New y-coordinate of F = -5 * (1/5) = -1
- Therefore, the new coordinates of F remain the same as (0, -1).
In summary, after the dilation with a scale factor of 1/5 and a center point at the origin (0,0):
- Point D(-5,5) is transformed to (-1,1).
- Point E(-10,-5) is transformed to (-2, -1).
- Point F(0,-5) remains the same as (0, -1).
This means that the angle DEF is dilated to a smaller angle, with its vertices at (-1,1), (-2,-1), and (0,-1), respectively.