Question

In reperul cartezian ( O;i;j ) se dau punctele A(2,2);B(3,5);C(2,-1) . Sa se determine :
a) Coordonatele punctului D stiind ca AD=3CB
b) Coordonatele punctului E stiind ca 3BE-5AC=0.

Answer 1

A(2;2) B(3;5) C(2;-1)

a) AD(xd-xa ; yd-ya)
AD(xd-2 ; yd-2)
AD = (xd-2)i+(yd-2)j

CB(xb-xc ; yb-yc)
CB(3-2 ; 5+1)
CB(1 ; 6)
CB = i+6j

AD = 3CB
(xd-2)i+(yd-2)j = 3(i+6j)
(xd-2)i+(yd-2)j = 3i+6j

xd-2 = 3
xd = 5.

yd-2 = 6
yd = 8.

D(5 ; 8).



b) 3BE-5AC = 0

BE(xe-xb ; ye-yb)
BE(xe-3 ; ye-5)
BE = (xe-3)i+(ye-5)j

AC(xc-xa ; yc-ya)
AC(2-2 ; -1-2)
AC(0 ; -3)
AC = -3j.

3(xe-3)i+3(ye-5)j+15j = 0
3(xe-3)i+3(ye-5)j = -15j.

3xe-9 = 0
3xe = 9
xe = 3.

3ye-15 = -15
3ye = 0
ye = 0.


E(3 ; 0).





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