Question
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)
(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)
Answers
GPT 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).
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).