calculus
posted by Carl .
What is the length of the blue line labeled r in the image below? Give your answer in terms of a and b.
blue line labeled r starting at the origin and ending at a point a,b
b
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 r / 
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_____________a

I am as frustrated as you are, because I can make very nice printerplots as you did, but HTML here does not accept Courrier font and always suppresses multiple spaces.
To answer your question, the length of a line that goes from (0,0) to (a,b) can be calculated by the standard distance formula,
Distance = sqrt((x2x1)^2+(y2y1)^2)
which is based on the Pythagoras formula.
For the given case, (x1,y1)=(0,0) and (x2,y2)=(a,b) so the distance reduces to
distance=sqrt(a²+b²)
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