Question

How do you find parametric equations to represent the line segment from (-3,2) to (1,-8)?

Answer 1

#{ (x =5 lambda -8), (y = lambda + 1) :}#

for `0 le lambda le 1`

Explanation:

Given two points `p_1,p_2` the segment between them is descrived as

`s = lambda p_1 + (1-lambda)p_2` for `0 le lambda le 1`

In the present case we have

#{ (x = lambda (-3) + (1-lambda)(-8) = 5 lambda -8), (y =lambda 2+(1-lambda) 1 = lambda + 1) :}#