which of the following vertex for the image produced by a dilatation about the origin with scale factor of 1/2
14.24
9.14
0.6
3,3.5
To determine the vertices after a dilation about the origin with a scale factor of 1/2, we multiply the coordinates of each vertex by the scale factor.
Let's look at each vertex:
1) (14, 24)
The dilated coordinates would be (14 × 1/2, 24 × 1/2) = (7, 12).
2) (9, 14)
The dilated coordinates would be (9 × 1/2, 14 × 1/2) = (4.5, 7).
3) (0, 6)
The dilated coordinates would be (0 × 1/2, 6 × 1/2) = (0, 3).
4) (3, 3.5)
The dilated coordinates would be (3 × 1/2, 3.5 × 1/2) = (1.5, 1.75).
Therefore, the correct option is 1.5, 1.75.
To find the new coordinates of a vertex after a dilatation about the origin with a scale factor of 1/2, you need to multiply each coordinate of the vertex by the scale factor.
Let's analyze the given vertices one by one:
1. (14, 24):
For this vertex, the new x-coordinate would be 14 * (1/2) = 7, and the new y-coordinate would be 24 * (1/2) = 12. Therefore, the new vertex is (7, 12).
2. (9, 14):
The new x-coordinate would be 9 * (1/2) = 4.5, and the new y-coordinate would be 14 * (1/2) = 7. Therefore, the new vertex is (4.5, 7).
3. (0, 6):
The new x-coordinate would be 0 * (1/2) = 0, and the new y-coordinate would be 6 * (1/2) = 3. Therefore, the new vertex is (0, 3).
4. (3, 3.5):
The new x-coordinate would be 3 * (1/2) = 1.5, and the new y-coordinate would be 3.5 * (1/2) = 1.75. Therefore, the new vertex is (1.5, 1.75).
Therefore, the correct answer is option 3: (0, 3).
To determine the vertex for the image produced by a dilation about the origin with a scale factor of 1/2, we need to understand how dilations work.
A dilation is a transformation that changes the size but not the shape of a figure. When dilating a point about the origin, the distance between the point and the origin is multiplied by the scale factor to determine the new location of the point.
In this case, the scale factor is 1/2, which means we need to multiply the distance between the given point and the origin by 1/2 to find the corresponding image point.
Let's calculate the new coordinates for each given point:
For the first option, 14.24:
x-coordinate_new = 14.24 * 1/2 = 7.12
y-coordinate_new = 14.24 * 1/2 = 7.12
The new coordinates would be (7.12, 7.12).
For the second option, 9.14:
x-coordinate_new = 9.14 * 1/2 = 4.57
y-coordinate_new = 9.14 * 1/2 = 4.57
The new coordinates would be (4.57, 4.57).
For the third option, 0.6:
x-coordinate_new = 0.6 * 1/2 = 0.3
y-coordinate_new = 0.6 * 1/2 = 0.3
The new coordinates would be (0.3, 0.3).
For the fourth option, (3, 3.5):
x-coordinate_new = 3 * 1/2 = 1.5
y-coordinate_new = 3.5 * 1/2 = 1.75
The new coordinates would be (1.5, 1.75).
Therefore, among the given options, the vertex for the image produced by a dilation about the origin with a scale factor of 1/2 is (1.5, 1.75).