How do you find the parametric equations for a line segment?

1 Answer
Wataru
Sep 6, 2014

The line segments between (x_0,y_0) and (x_1,y_1) can be expressed as:
x(t)=(1-t)x_0+tx_1
y(t)=(1-t)y_0+ty_1,
where 0 leq t leq 1.

The direction vector from (x_0,y_0) to (x_1,y_1) is
vec{v}=(x_1,y_1)-(x_0,y_0)=(x_1-x_0,y_1-y_0).
We can find any point (x,y) on the line segment by adding a scalar multiple of vec{v} to the point (x_0,y_0). So, we have
(x,y)=(x_0,y_0)+t(x_1-x_0,y_1-y_0),
which simplifies to:
(x,y)=((1-t)x_0+tx_1,(1-t)y_0+ty_1),
where 0 leq t leq 1.

Related questions
See all questions in Introduction to Parametric Equations
Impact of this question
31534 views around the world
You can reuse this answer
Creative Commons License