Question

considerando o segmento AB, com A(2,4) e B(10,9), determine o ponto P do segmento AB tal que AP/PB=3/5

Answer 1

$\frac{AP}{PB}=0,6$

 

$\frac{P-A}{B-P}=0,6$

 

$P-A=0,6B-0,6P$

 

$P+0,6P=0,6B+A$

 

$1,6P=0,6B+A$

 

$P=\frac{0,6B+A}{1,6}$

 

$P=0,375B+0,625A$

 

Substituindo:

 

$P=0,375(10;9)+0,625(2;4)$

 

$P=(3,75;3,375)+(1,25;2,5)$

 

$\boxed{P=(5;5,875)}$