Parametrising a line segment

Problem

Write a parametrisation of the segment with endpoints $(0,0)$ and $(4,3)$ with $t\in[0,1]$.

Solution

A segment from $P_0$ to $P_1$ is parametrised by linear interpolation: $P(t)=P_0+t\,(P_1-P_0)$, with $t\in[0,1]$. With $P_0=(0,0)$ and $P_1=(4,3)$: $\begin{cases} x(t) = 4t \\ y(t) = 3t\end{cases}, \quad t\in[0,1].$ For $t=0$ we obtain $(0,0)$, for $t=1$ we obtain $\boxed{(4,3)}$; the intermediate points trace out the segment.

Links

Topics: Complex numbers
Concepts: Parametrisation
Skills: Modelling
Exercise type: Modelling problem