Question

C. Find a parametrization for the line segment with endpoints (-1, 3) and (3, -2).

Answer 1

x(t) = -1 + 4t

y (t) = 3 - 5t

Explanation:

The end points of the line segment are (-1, 3) and (3, -2).

Let a = (-1,3) and b = (3,-2)

Now, find the value of (b-a)

(b-a) = ((3+1), (-2-3))

b-a = (4, -5)

Therefore, the parametrization of the given line segment is

r(t) = a + (b-a)t

r(t) = (-1,3) +(4,-5)t

r(t) = (-1+4t, 3-5t)

We can rewrite this as

x(t) = -1 + 4t

y (t) = 3 - 5t