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 find the image of a point after a dilation about the origin, we need to multiply its coordinates by the scale factor.
In this case, the scale factor is missing, so we cannot determine the correct answer.
To find the image produced by a dilation about the origin with a scale factor, we need to multiply the coordinates of each vertex by the scale factor.
Given that the scale factor is not provided in the question, we cannot determine the correct answer without that information. Could you please provide the scale factor?
To determine the vertex of the image produced by a dilation about the origin with a scale factor, we can use the formula:
(x', y') = (k * x, k * y)
where (x', y') is the coordinates of the image, (x, y) is the coordinates of the original point, and k is the scale factor.
Let's calculate the coordinates of the image for each of the given points using a scale factor of k:
A. (21, 3)
(x', y') = (k * 21, k * 3) = (21k, 3k)
B. (10, 6)
(x', y') = (k * 10, k * 6) = (10k, 6k)
C. (2, 10)
(x', y') = (k * 2, k * 10) = (2k, 10k)
D. (12, 0)
(x', y') = (k * 12, k * 0) = (12k, 0)
Now, let's compare the calculated image coordinates with the given vertices of the parallelogram:
Original vertices:
(0, 0), (18, 0), (24, 30), (6, 30)
Comparing with A:
(21k, 3k)
Comparing with B:
(10k, 6k)
Comparing with C:
(2k, 10k)
Comparing with D:
(12k, 0)
None of the calculated image coordinates match the given vertices of the parallelogram. Therefore, none of the points A, B, C, or D is a vertex for the image produced by a dilation about the origin with a scale factor.