The vertices of a parallelogram are shown below.
(0 , 0), (18 , 0), (24 , 30), (6 , 30)
Which of the following points is a vertex for the image produced by a dilation about the origin with a scale factor of ?
A. (21 , 3)
B. (10 , 6)
C. (2 , 10)
D. (12 , 0)
To perform a dilation about the origin with a scale factor of k, each coordinate (x, y) of a point is multiplied by k.
In this case, let's consider the dilation with a scale factor of k = 2.
For the point (0, 0), the dilation will just be (0, 0) because any point multiplied by 2 will still be at the origin.
For the point (18, 0), the x-coordinate is multiplied by 2, giving us (36, 0).
For the point (24, 30), both the x and y-coordinates are multiplied by 2, giving us (48, 60).
For the point (6, 30), the x-coordinate is multiplied by 2, giving us (12, 30).
Out of the given options, the point (12, 0) is a vertex of the image produced by the dilation about the origin with a scale factor of 2.
Therefore, the correct answer is D. (12, 0).
To find the image of a dilation about the origin, we need to multiply the coordinates of each vertex by the scale factor.
The scale factor is missing in the question, so we need to use the actual scale factor to determine the image.
Please provide the value of the scale factor.
To find the image produced by a dilation about the origin with a scale factor of k, we multiply the coordinates of each vertex by the scale factor k. In this case, the scale factor is missing in the question, so we cannot determine the answer without it.
Please provide the missing scale factor so that I can help you find the corresponding vertex for the image.