Homogeneous representation of the line passing through the points

Question

I got the task calculate the homogeneous representation of the line passing through the points (-4, 0) and (−2, 2) and to visualize the situation by drawing the lines and points in a 2D cartesian coordinate system.

I am getting confused between the homogeneous representation and the euclidean one... How should I calculate this?

Answer 1

You solve the two equations (dot product of the two points and the generic form of homogeneous line): u*-4 + v*0 + g*1 = 0 u*-2 + v*2 + g*1 = 0

to get the relation between the three parameters of the representation: u = - v 4v = -g

Then you can pick a value for say g: g = 1 v = -1/4 u = 1/4

You can confirm this particular homogeneous line passes through the two point by calculating the dot products.