Parametric Equations: Deriving (1-t)

[Marioqwe]

So, the parametric equations of a line segment from (x0,y0,z0) to (x1,x2,x3) are

x = (1-t)x0 + tx1
y = (1-t)y0 + ty1
z = (1-t)z0 + tz1


right?

But how are these equations derived? I don't really see where the (1-t) is coming from.
I would be really thankful if anybody could explain this to me.

 

[tiny-tim]

Hi Marioqwe!

(try using the X₂ icon just above the Reply box )

It's because it's really

x = x₀ + t(x₁ - x₀)
y = y₀ + t(y₁ - y₀)
z = z₀ + t(z₁ - z₀)

 

[Marioqwe]

Didn't catch that. Thank you very much.