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

1 Answer
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#.