transformation

zxteh

1.)The point P,Q,and R are three colinear points on a cartesian plane and T(P)=P1,T(Q)=Q1 and T(R)=R1,where T:R^2->R^2 is a linear transformation. If PQ:QR=a:b,find P1Q1:Q1R1.

dunwan2tellu

PQ = a/(a+b) * PR

T(P)=P1,T(Q)=Q1 ==>T(PQ)=P1Q1

同样的 T(PR)=P1R1

所以 T(PQ)=T(a/(a+b)*PR) = a/(a+b)*P1R1
=> P1Q1 = a/(a+b) * P1R1

=> P1Q1:Q1R1 = PQ:QR = a:b

*注 : 在linear transformation 里 , T(v + w) = T(v) + T(w) . T = transformation from R^n to R^m . v,w = vector in R^n

[ 本帖最后由 dunwan2tellu 于 13-11-2007 12:11 PM 编辑 ]