A line segment is dilated by a scale factor of 2 centered at a point not on the line segment. Which statement regarding the relationship between the given line segment and its image is true?
A The line segments are parallel, and the image is twice the length of the given line segment.
B. The line segments are parallel, and the image is one-half of the length of the given line segment.
C. The line segments are perpendicular, and the image is twice the length of the given line segment.
DD The line segments are perpendicular, and the image is one-half of the length of the given line segment.

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  A The line segments are parallel, and the image is twice the length of the given line segment.

Step-by-step explanation:

Dilation by a factor of 2 means any measure of the image is 2 times the corresponding measure of the original.

Dilation does not change any orientations, so the image will have the same orientation with respect to the origin, axes, or any other line segments. That means the dilated segment is parallel to the original. (If the center of dilation is on the original line segment, the dilated segment will overlay the original segment. That is specifically not the case here.)

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation: