Question

O ponto A está em (-2,4) e o ponto C está (4,7).

Encontre as coordenadas do ponto B em AC tais que a razão entre AB e AC seja 1 : 3


B = ​

Answer 1

Resposta:

B(0, 5)

Explicação passo a passo:

A(-2, 4)                B(x, y)                              C(4, 7)

$\frac{AB}{AC} =\frac{1}{3} \\\\\frac{x_B-x_A}{x_C-x_A} =\frac{1}{3} \\\\\frac{x-(-2)}{4-(-2)} =\frac{1}{3}\\\\\frac{x+2}{4+2} =\frac{1}{3} \\\\3x+6=6\\\\3x=6-6\\\\3x=0\\\\x=0\\\\\\\frac{y_B-y_A}{y_C-y_A}=\frac{1}{3} \\\\\frac{y-4}{7-4} =\frac{1}{3}\\\\\frac{y-4}{3} =\frac{1}{3}\\\\y-4=1\\\\y=1+4\\\\y=5\\\\B(0,5)$