Apply the dilation d to the polygon with the given vertices. name the coordinates of the image points. identify and describe the transformation.
d: (x, y) → (4x,4y)
a (2,1) b (4,1) c (4,-3)

a. this is a dilation about (0, 0) with a scale factor of 0.25; a’(8, 4), b’(16, 4), c’(16, –12).

b. this is a dilation about (0, 0) with a scale factor of 4; a’(8, 4), b’(16, 4), c’(16, –12).

c. this is a dilation about (0, 0) with a scale factor of 0.25; a’(0.5, 0.25), b’(1, 0.25), c’(1, –0.75).

d. this is a dilation about (0, 0) with a scale factor of 4; a’(0.5, 0.25), b’(1, 0.25), c’(1, –0.75).

To solve this you just do ehat was done to the coordinates. So x goes from x to 4x do you are mutiplying by 4. and the same goes for y. so your scale factor is 4

2 times 4 is 8 and 1 times 4 is four

A(8,4)

4 times 4 is 16 and 1 times four is four

B(16,4)

Four times four is sixteen and negitive three times four is negitive 12

C(16,-12)

Given the options the answer will be B. 

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: