Rectangle ABCD is dilated to form rectangle A’B’C’D’. What is the dilation factor? What is the center of dilation? Select all that apply.
The figure shows two rectangles UpperWord ABCD and UpperWord A complement, B complement, C complement, and D complement on the coordinate grid. The values on the x-axis range from negative 12 to 6 in increments of 2 and the values on the y-axis range from negative 2 to 16 in increments of 2. The coordinates of the vertices Upper A, Upper B, Upper C, and Upper D are labeled as (negative 11, 14), (negative 5, 14), (negative 5, 10), and (negative 11, 10) respectively. The coordinates of the vertices Upper A complement, Upper B complement, Upper C complement, and Upper D complement are labeled as (negative 5, 8), (negative 2, 8), (negative 2, 6), and (negative 5, 6) respectively.
A.
dilation factor of 2
B.
dilation factor of
1
2
C.
center of dilation
(
1
,
2
)
D.
center of dilation
(
2
,
1
)
compare the lengths of sides. That will give you the dilation factor
... oobleck thx
thank you oobleck :)
A. dilation factor of 2
C. center of dilation (1, 2)
To determine the dilation factor and the center of dilation, we need to compare the corresponding side lengths of the original rectangle ABCD and the transformed rectangle A’B’C’D’.
For the dilation factor, we can calculate the ratio of the corresponding side lengths. Let's consider the horizontal side AB and its corresponding side A'B'. The length of AB is |(-11) - (-5)| = 6, and the length of A'B' is |(-5) - (-2)| = 3. The ratio between these lengths is 6/3 = 2. Therefore, the dilation factor is 2.
Now let's determine the center of dilation. To find the center of dilation, we need to identify the point which remains fixed during the dilation transformation. Comparing the coordinates of the vertices of ABCD and A’B’C’D’, we can see that the common point is (-5, 6). This means that (-5, 6) is the center of dilation.
Therefore, the correct options are:
A. Dilation factor of 2
D. Center of dilation (-5, 6)
when dealing with sets, ' does denote complement.
Usually when describing transformed figures, we just say A-prime, B-prime, etc.
Since AB=6 and A'B'=3, the dilation factor is 1/2
The center of dilation is (1,2) because the vertices of ABCD are twice as far away from (1,2) as are the vertices of A'B'C'D'