Question

1.) Decide if the following triples of points are non-collinear, and justify your answers. (a) 21 = (1.5, 4), 72 = (2.5, 3), 13 = (0.5, 1) in the cartesian plane R2. (b) x1 = L1 = R:(1,1,1), x2 = L2 = R:(2,3,4), x3 = L3 = R-(0,1,1) in RP2.

Answer 1

Au-1 f ttanyle Cmade the ee callneasdty pos)should not be 3o CI.S,4) 2 2.S,3) 2 4 A 2-S 1 0-S 1-S 4 1-sx3- 2Sx4) + (2-fx1- 0sxs)+ (osx4- 1-5X1)| 4--10)2-5-1-5)+ (2-1r)|| (9-13)1 = 2 Sq uds Area non collfheas ase - R (1,,1) y R (0,1\,\)

Dis tan ce betoeau poinis. Dishnce b _& eggj- (o-2)2-3)21-4)2 N44+9 Distance blo Xg exc) Co-) +(1-+)2 +CI-iY 1 toto Distance ba He otte two + A+ BIC diotances betweu Guy troo penks pon Sun A+BC a A te +B Points ahe not collineat .