Let c = (u,v)', X = (x,y,λ)', and Q = |  α   β  | |  γ   δ  | Then |  α   β   u  | |x| | αx+βy+λu | TX = |  γ   δ   v  | |y| = | γx+δy+λv | |  0   0   0  | |λ| | λ | We see immediately that T maps Π : z=λ to itself. If we ignore the z-coordinate (concentrating of the map from Π to itself), we see that the map sends (x,y) to (αx+βy+λu,γx+δy+λv). As b=λc, this is exactly the effect of the euclidean map on R2 taking x to Qx+b, .

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