The preimage ∆ABC has points at A(2,-2), B(5,-4), and C(1,-6) and is dilated by a certain scale factor from a certain center of dilation. The image of ∆A'B'C' has points at A'(-6,8), B'(3,2), and C'(-9,-4). Use only algebraic reasoning (NO GRAPHING) to find the coordinates of the center of dilation. Show all work used below and provide a complete written justification for your answer. Explain what you did and why you did it.

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:

what graph

step-by-step explanation: