Rectangle CDEF undergoes a dilation centered at the origin. The result is rectangle C'D'E'F'. Which rule describes the dilation?
Responses
A (x, y) → (2x, 2y)(x, y) → (2x, 2y)
B (x, y) → (4x, 4y)(x, y) → (4x, 4y)
C (x, y) → (−12
x, −12
y)(x, y) → (− 1 2 x, − 1 2 y)
D (x, y) → (12
x, 12
y)
B (x, y) → (4x, 4y)
The correct answer is:
D (x, y) → (12x, 12y)
To determine the rule for the dilation of rectangle CDEF to C'D'E'F', we need to analyze the transformation of the points.
A dilation is a transformation that uniformly scales all dimensions of an object. The dilation rule determines how much the x-coordinates and y-coordinates of the points change.
In rectangle CDEF, let's consider the point C with coordinates (x, y).
After the dilation, the corresponding point will be C' with coordinates (x', y').
To find the dilation rule, we can compare the coordinates of C and C'.
From the given answer choices:
A) (x, y) → (2x, 2y)
B) (x, y) → (4x, 4y)
C) (x, y) → (-12x, -12y)
D) (x, y) → (12x, 12y)
Let's apply each rule to the coordinates of point C and check if the transformed coordinates match C'.
A) Using rule (x, y) → (2x, 2y):
C' = (2x, 2y)
B) Using rule (x, y) → (4x, 4y):
C' = (4x, 4y)
C) Using rule (x, y) → (-12x, -12y):
C' = (-12x, -12y)
D) Using rule (x, y) → (12x, 12y):
C' = (12x, 12y)
Comparing the coordinates of C' to the given C'D'E'F', it appears that none of the options accurately describe the dilation. Therefore, none of the given choices (A, B, C, D) are correct.
Alternatively, if there is additional context or information that was not provided, it could be helpful in determining the correct dilation rule.