Question

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

Answer 1

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`.