Question

Dados A(-3, -5) e B(1, -1), determine o ponto
C(x, y) que divide o segmento orientado AB
na razão -7/3

Answer 1

Resposta:

AB²=(1+3)²+(-1+5)² =16+16   ==>AB=4√2

AC+BC=4√2  

AC/BC = 7/3  ==>AC=7BC/3

7BC/3+BC=4√2

7BC+3BC=12√2

BC =6√2/5   e  AC =42√2/15

AC²=(-3-x)²+(-5-y)²=(42√2/15)²  ==>(-3-x)²+(-5-y)² =3528/225

CB²=(1-x)²+(-1-y)²=(6√2/5 )² ==>  (1-x)²+(-1-y)²=72/25 =648/225

9+6x+x²+25+10y+y² = 3528/225  (i)

1-2x+x² +1+2y+y² = 648/225  (ii)

(i)-(ii)

32 +8x+8y  =  2880/225

x+y  =360/225 -4

x+y =-2,4  ==>x =-2,4 -y   (iii)

(iii)  em (i)

9+6*(-2,4 -y)+(-2,4 -y)² +25+10y+y² = 3528/225

y=-2,2   e x= x =-2,4 +2,2 =- 0,2

Ponto (-0,2 ; -2,2)