Question

9. (a) Find a parametrization for the line segment from the point (-1, 2) to the point (3,-2). (b) Find the length of the line segment using techniques learned in chapter 11. (Note: No credit will be given for using the Pythagorean theorem to find the length).

Answer 1

al construct he can is proscimetric functions are then then given a To line porometric functions for segment starting at ca,b) and ending at (c,d) start cat (a, b) and travel along the displacement vector to cc,d). The displacement vector <c, d)-(a,b) = <c-and-b) And the by Kalt), y(t)) = (a,b) + tlca, d-b) osts 1 So start at (-1, 2) and then travel along the displacement vector to (3,-2). The displacement vector is given by: <3,-2) - (-1, 2) =(4,-4) And thus the parametric equations are Lact), y(t)) (-1, 2) + t <4,-4) (act), y(t)) (-1+ht, 2-ut) ; ostsi

(6) The length of parametric curve is given by b 2 2 dal It + N dt a Ser from Purt (a) at t dy -4 & octçi dt 1 So, Le (4)²+(-4² at 0 11 J2x16 dt ар 1 = 482 It 1 0 452 Lt 452 [1-o = L = 482 So, the length of line segment å 412. Hope this is helpful!