Let P and Q be points in R 2 . Show that a linear map (u, v) = (Au + Cv, Bu + Dv) maps

Let P and Q be points in R². Show that a linear map Φ(u, v) = (Au + Cv, Bu + Dv) maps the segment joining P and Q to the segment joining Φ(P) to Φ(Q). The segment joining P and Q has parametrization

(1-1)0P + 100 for 0t1