Figure abcs is rotated 90 degrees counter clock wise about the origin. which of the following gives the correct measure if an image if one of its sides?

Nothing here makes sense.

-- The question talks about "Figure ABCS", but the picture is ABCD .
Where is 'S' ?

OK. Let's assume that it's really talking about Figure ABCD. Then
the whole problem is loaded with nonsense and red herrings.

-- When a figure is rotated, translated, or both rotated AND translated,
why should the length of any of its sides change ?  You can just as well
forget all about the rotation, and just check out the length of the sides
as they sit in the drawing.

-- The third choice is there just to see who has a clue and who has none.
What in the world is "DD" ? It may apply to an article of women's clothing,
but it certainly has no relevance to this drawing.  The distance from 'D' to
'D' is zero.

-- The side BC is 1 unit wide and 3 units high.
Its length is √(1+ 9) = √√10 .
So the first choice is not true.

--  The side CD is 4 unit wide and 1 unit high.
Its length is √(16 + 1) = √17.
The second choice is true.

But wait !  Don't go away.

-- As we've said, "DD" is a zero distance.
So the third choice is nonsense.

-- Side AB is 4 units wide and 1 unit high.
Its length is √(16 + 1) = √17 .
The fourth choice is also true.