Question

Rectangle CDEF undergoes a dilation centered at the origin. The result is rectangle C'D'E'F'. Which rule describes the dilation?
A) (x, y) → (2x, 2y)
B) (x, y) → (4x, 4y)
C) (x, y) → (−1/2x, -1/2y)
D)(x,y) → ( 1/2x, 1/2y)

Answer 1

Answer:

D)(x,y) → ( 1/2x, 1/2y)

Step-by-step explanation:

FE goes from x = -8 to x = 10.  This makes the length of FE 18.

ED goes from y = 2 to y = -8.  This makes the length of ED 10.

F'E' goes from x = -4 to x = 5.  This makes the length of F'E' 9.

E'D' goes from y = 1 to y = -4.  This makes the length of E'D' 5.

Comparing FE to F'E', we see that F'E' is half the length of FE.

Comparing ED to E'D', we see that E'D' is half the length of ED.

This means the dilation has a scale factor of 1/2; this means the rule is (x,y) → ( 1/2x, 1/2y)

Answer 2

Rectangle CDEF undergoes a dilation centered at the origin. The result is rectangle C'D'E'F'. The rule for which it describes the dilation will be :-

(x,y) → ( 1/2x, 1/2y)

Given : Two Rectangles given in the diagram , CDEF & C'D'E'F'

According to the questions, informations as follows

• FE goes from {x = -8 to x = 10}  Then,  the length of FE 18.

• ED goes from {y = 2 to y = -8}  Then,  the length of ED 10.

• F'E' goes from {x = -4 to x = 5} Then, the length of F'E' 9.

• E'D' goes from {y = 1 to y = -4} Then, the length of E'D' 5.

On Comparing length wise FE to F'E',

F'E' = $\rm \dfrac{1}{2}$ FE

On Comparing length wise ED to E'D',

E'D' = $\rm \dfrac{1}{2}$ ED.

Therefore, the dilation has a scale factor half i.e. the rule is

(x,y) → ( 1/2x, 1/2y)

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