Let A = (−6, −4), B = (3, 2), and C = (6, 4).

Question

(a)These points lie on a line through the origin. Find its slope.
(b)Let u be the vector whose components are the x-coordinates of A, B, and C, and let v
be the vector whose components are the y-coordinates of A, B, and C. Show that v is a
positive scalar multiple of u (thus u and v point in the same direction).
(c)Explain why the scalar multiple in part (b) equals the slope you found in part (a).
(d)What would the vectors u and v have looked like if A, B, and C had not been collinear
with the origin?

Answer 1

slope of AB is (2+4)/(3+6) = 2/3
since the slope is 2/3, v = 2/3 u

if the points started at (h,k) then there'd be an offset of
u = u+h
v = v+k