Question

Sendo A (1,-1) e B(-3,7), determine os pontos C, D e E que dividem o seguimento AB em quatro partes de mesmo comprimento

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Answer 1

Resposta:

Explicação passo a passo:

A____________C____________D__________E___________B

São 4 segmentos iguais.

$\frac{AC}{AB} =\frac{x_C-x_A}{x_B-x_A}\\\\\frac{1}{4} =\frac{x_C-1}{-3-1}\\\\4x_C-4=-4 \\\\4x_C=-4+4\\\\4x_C=0\\\\x_C=0\\\\\frac{AC}{AB}=\frac{y_C-y_A}{y_B-y_A}\\\\\frac{1}{4}=\frac{y_C+1}{7+1} \\\\4y_C+4=8\\\\4y_C=8-4\\\\4y_C= 4\\\\y_C=\frac{4}{4}\\\\y_C=1\\\\C(0,1)$

$\frac{1}{2}=\frac{x_D-1}{-3-1} \\\\2x_D-2=-4\\\\2x_D=-2\\\\x_D=-1\\\\\frac{1}{2}=\frac{y_D+1}{7+1} \\\\2y_D+2=8 \\\\2y_D=6\\\\y_D=3\\\\D(-1,3)$

$\frac{3}{4} =\frac{x_E-1}{-3-1} \\\\4x_E-4 = -12\\\\4x_E=-8\\\\x_E=-2\\\\\frac{3}{4} =\frac{y_E+1}{7+1} \\\\4y_E+4=24\\\\4y_E=20\\\\y_E=5\\\\E(-2,5)$