Question

Find the final point for P(5, 8) if the point is rotated 60° and translated at (-6, 9) and finally is scaled with scaling factor of (2, 0.5)

Answer 1

Given dată is, point P (5,8) is (i) votated by ooº, let point offer rotation be p, P,- RiP R- ootational matrix (in) translated or (-6,9), let point aflês translation by 'B [P2 = T.P.] P = T.R.P] Tz translation matrix (ii) then scaled with scaling factor of (2,0.5), let the final point after scaling be "Pg". (P = S.P2 s= scaling matrix P₂ = S.T.R.PL P = RP R= cose -sino of sine coso ol to where 0=60 2. Cos 60 - Simbo 0757 sin 60 costo => P. 10.5 -0.866 01757 (0.5x5 + f0:866x8 )+07 0.866 0.5 0|1 0.866*5)+ (0.5*8) +0 lo 0 TL'Lo + 0 + i] 3D p. P - -4.4287 8.33 =D P, = (-4428,8.33)

(ii) translation of Pi T Op7 "Joia (8,9)-(-6,9) -D 0 *** 0 -671-4.4287 -4.428+0-67 loi 41 8.33 : 0 + 8.33 +9 Tool ++] 3D P = -10.4287 17.33 -D B- (-10.428,17.33) (fi) scaling of Pa scaling factor Pg= 5.B SofWa007 Tolly ol Looi =P Pa [20 077-10.4287 Mx, My = 2,0.5 O 0.50 19 33 (2x-10-428) + 0 +0 7 0 + (0.5X17-33) +0 E 0 + 0 + 1] - 20.856 8.665 (-20-856, 8.665) Answer Therefore, final point offer transformalion i.e., volation, translation scaling is '(-20.856, 8.665)"