Again, I wish I could type it to cut down on the picture questions, but any help is appreciated!! I believe the answer is 6, but I am not so sure.

LaughingFace
Apr 26, 2018

#2**+3 **

The answer is 6.....to see this....let C = (0, 0) and let D = (9, 0)

[These are arbitrary...we can pick any two points that are 9 units apart ]

Then CD = 9

The first transformation doesn't do anything to the length....it just shifts C to the right 3 units and down 2 units ...so.... C' = (3, - 2)

And it does the same to D.....so we have D' = (12, - 2)

The second transformation is applied to both of these points.....so

C'' = (2/3)(3, - 2) = (2, - 4/3)

And D'' = (2/3)(12, - 2) = ( 8, - 4/3)

And the distance between these points is

sqrt [ (8 - 2)^2 + ( -4/3 - - 4/3)^2 ] =

sqrt [ 6^2 + 0^2 ] =

sqrt [ 36 ] =

6 .....just as we suspected !!!!!!

CPhill
Apr 26, 2018