Question

O ponto P(5; $\frac{14}{3}$) está entre A(3;6) e B(x;y) de tal forma que $\frac{AP}{PB}= \frac{1}{2}$. As coordenadas do ponto B são:
a) -9 e -2
b) -9 e 2
c) 9 e -2
d) 9 e 2
e) -1 e 2

Answer 1

temos do enunciado que:

$\frac{AP}{PB}= \frac{1}{2} -\ \textgreater \ PB=2AP-\ \textgreater \ B-P=2(P-A)-\ \textgreater \ B-P=2P-2A$$-\ \textgreater \ B=3P-2A-\ \textgreater \ (X,Y)=3(5, \frac{14}{3} )-2(3,6)-\ \textgreater$$(X,Y)=(15,14)-(6,12) -\ \textgreater \ \left \{ {{X=15-6} \atop {Y=14-12}} \right. -\ \textgreater \ \left \{ {{X=9} \atop {Y=2}} \right.-\ \textgreater \ B=(9,2)$ portanto a letra D e a correta!!