How do you find the length of the line #x=At+B, y=Ct+D, a<=t<=b#?

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Answer 1 · 2018-03-04T11:45:18

#l = abs(a-b)sqrt(A^2+C^2)#

Given the line

#L -> p = p_0 + vec v t#

with

#p = (x,y)#
#p_0 =(B,D)#
#vec v = (A,C)#

we have

#p_a = p_0 + vec v a#
#p_b = p_0 + vec v b#

and then

#l = norm(p_a-p_b)= norm(p_0+ (vec v) a - p_0 - (vec v) b) = norm(vec v(a-b)) = abs(a-b)norm (vec v) = abs(a-b)sqrt(A^2+C^2)#