The vertices of a trapezoid are shown below.
(0,6), (7,12), (7,9), (0,12)
Which of the following points is a vertex for the image produced by a dilation about the origin with a scale factor of 1/2?
(14,24)
(9,14)
(0,6)
(3,3.5)
To perform a dilation about the origin with a scale factor of 1/2, we multiply the x-coordinates and y-coordinates of each point by 1/2.
For the point (0,6), the dilation would result in (0*(1/2), 6*(1/2)) = (0,3).
For the point (7,12), the dilation would result in (7*(1/2), 12*(1/2)) = (3.5,6).
For the point (7,9), the dilation would result in (7*(1/2), 9*(1/2)) = (3.5,4.5).
For the point (0,12), the dilation would result in (0*(1/2), 12*(1/2)) = (0,6).
Out of the given points, the point (3,3.5) is the result of the dilation and it is a vertex for the image produced by a dilation about the origin with a scale factor of 1/2.
Therefore, the correct answer is (3,3.5).
To find the vertex of the image produced by a dilation about the origin with a scale factor of 1/2, you need to multiply each coordinate of the original vertex by the scale factor.
Let's apply the scale factor of 1/2 to each of the original coordinates and see which option matches.
For the first vertex (0,6), applying the scale factor gives us:
(0 * 1/2, 6 * 1/2) = (0, 3)
For the second vertex (7,12):
(7 * 1/2, 12 * 1/2) = (3.5, 6)
For the third vertex (7,9):
(7 * 1/2, 9 * 1/2) = (3.5, 4.5)
For the fourth vertex (0,12):
(0 * 1/2, 12 * 1/2) = (0, 6)
Among the provided options, the point that matches the coordinates we obtained after applying the dilation is (3.5, 6).
Therefore, the correct answer is (3, 7.5).
To find the image produced by a dilation about the origin with a scale factor of 1/2, you need to multiply the coordinates of each vertex by the scale factor.
Let's multiply the coordinates of each vertex by 1/2:
For the vertex (0,6), multiplying both coordinates by 1/2 gives us (0*(1/2), 6*(1/2)) = (0,3).
For the vertex (7,12), multiplying both coordinates by 1/2 gives us (7*(1/2), 12*(1/2)) = (3.5,6).
For the vertex (7,9), multiplying both coordinates by 1/2 gives us (7*(1/2), 9*(1/2)) = (3.5,4.5).
For the vertex (0,12), multiplying both coordinates by 1/2 gives us (0*(1/2), 12*(1/2)) = (0,6).
Now we have the coordinates of the vertices of the image produced by the dilation.
Out of the given points, (3,3.5) corresponds to the vertex (7,9) after the dilation.
Therefore, the answer is (3,3.5).