Let A(a1,a2) and B(b1,b2) be two points in the plane
and let σ be the line segment from A to B. Recall that the standard “convex combination”to parameterize σ when 0 ≤t ≤1, is with the parametric equations:
x(t) = a1(1 −t) + b1t
y(t) = a2(1 −t) + b2t
1)For a positive real number t1, find a parameterization of σ where t1 ≤t ≤(t1 + 1).
2)For a positive real number t2, find a parameterization of σ where 0 ≤t ≤t2.
3)For two positive real numbers t1 and t2, find a parameterization of σ where t1 ≤t ≤t2.