Noah has drawn two triangle △mno and △m'n'o' on the coordinate plane as shown below. (the image i pasted)

which statement is the best explanation of the relationship between these triangles?

a. the given triangles are similar because they can be mapped onto each other by a series of reflections, translations, and dilations.

b. the given triangles are similar because they can be mapped onto each other by a series of reflections, translations, and rotations.

c. the given triangles are not similar because they cannot be mapped onto each other by a series of reflections, translations, and dilations.

d. the given triangles are not similar because they cannot be mapped onto each other by a series of reflections, translations, and rotations.

*i think the answer is c because the dilation doesn't add right but i'm not sure

so i want to check with you guys, by the way this is geometry

ignore the college, this is high school

  choice C is correct

Step-by-step explanation:

The clockwise sequence of vertices MNO is the opposite of the counterclockwise sequence of vertices M'N'O', so it seems some sort of reflection is involved.

Length NO is 3 times length N'O', but length NM is only 7/3 times length N'M', so the figures are not similar. (The ratios of side lengths must be the same for the figures to be similar.)

___

Choice D includes only rigid transformations that would ensure congruence. Similar figures may also differ by a dilation factor, so C is the better choice.

there is no image attacted

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: