In class, we discussed the concept of homogeneous coordinates. In this example, we will confine ourselves to the real 2D plane, A point (x,y) on the real 20 plane can be represented in homogeneous coordinates by a 3-vector (wx,wy,w), where w=0 is any real numbec. All values of w=0 represent the same 2D point. Dividing out the third coordinate of a homogeneous point (x,y,z) converts it back to its 2D equivalent: (zx,zy). Consider a line in the 20 plane, whose equation is given by ax+by+c=0. This can equivalently be written as Ix=0, where I=(a,b,c) and x=(x,y,1). Noticing that x is a homogeneous representation of (x,y), we define I as a homogeneous representation of the line ax+by+c=0. Note that the line (ka)x+(kb)y+(kc)=0 for k=0 is the same as the line ax+by+c=0, so the homogeneous representation of the line ax+by+c=0 can be equivalently given by (a,b,c) or (ka,kb,kc) for any k=0. All points (x,y) that lle on the line ax+by+c=0 satisfy the equation Ix=0, thus, we can say that a condition for a homogeneous point x to lie on the homogeneous line I is that their dot product is zero, that is, Ix=0. We note this down as a fact: Fact 1: A point x in homogeneous coordinates lies on the homogeneous line 1 if and only if xl=1x=0 Now let us solve a few simple examples: - 3(a) Glve at least two homogeneous representations for the point (3,5) on the 2D plane, one with w>0 and one with w0 and one with w