Which statement is part of the proof that the dilation of 

CD
¯
¯
¯
¯
¯
¯
¯
¯
 with a scale factor of 
1
3
 and a center of dilation at the origin will result in a line segment that is 
1
3
 the length of 
CD
¯
¯
¯
¯
¯
¯
¯
¯
?

The statement that is part of the proof is: "The length of the dilated line segment is equal to the scale factor multiplied by the length of the original line segment."

how many units is it dumby

If the original line segment CD¯ has a length of 9 units, then the dilated line segment will have a length that is 1/3 of CD¯, which is (1/3) * 9 = 3 units. So, the dilated line segment will be 3 units long.