Respuesta:
Explicación paso a paso:
creo que tienes un 4 de más.
Pero lo haremos con las dos opciones
a) (-2 , 3a), 4(4, -a), m = -5/12
quedarían los puntos (-2, 3a), (16, -4a), m = -5/12
m = [tex]\frac{y_{2}- y_{1} }{x_{2} -x_{1} }[/tex] = [tex]\frac{-4a - 3a}{16 - (-2)} = \frac{-7a}{16+2} = \frac{-7a}{18}[/tex]
pero m = -5/12
luego : [tex]-\frac{5}{12} = \frac{-7a}{18}[/tex] despejo a
a = [tex]-(\frac{5}{12}) *(-\frac{18}{7} )= (\frac{5}{2})*(\frac{3}{7}) = \frac{15}{14}[/tex]
comprobación
m = [tex]\frac{y_{2}- y_{1} }{x_{2} -x_{1} }[/tex] = [tex]\frac{-4*(\frac{15}{14}) - 3*\frac{15}{14} }{16 - (-2)} = \frac{-7*\frac{15}{14} }{16+2} = \frac{\frac{-15}{2} }{\frac{18}{1} } = -\frac{15}{36} = -\frac{5}{12}[/tex]
b) (-2, 3a), (4, -a), m = -5/12
m = [tex]\frac{y_{2}- y_{1} }{x_{2} -x_{1} }[/tex] = [tex]\frac{-a - 3a}{4 - (-2)} = \frac{-4a}{4+2} = \frac{-4a}{6}[/tex] = [tex]- \frac{2}{3}a[/tex]
pero m = -5/12
luego : [tex]-\frac{5}{12} = \frac{-2a}{3}[/tex] despejo a
a = [tex]-(\frac{5}{12}) *(-\frac{3}{2} )= (\frac{15}{24}) = \frac{5}{8}[/tex]
comprobación
m = [tex]\frac{y_{2}- y_{1} }{x_{2} -x_{1} }[/tex] = [tex]\frac{-(\frac{5}{8}) - 3*\frac{5}{8} }{4 - (-2)} = \frac{-4*\frac{5}{8} }{4+2} = \frac{\frac{-20}{8} }{\frac{6}{1} } = -\frac{20}{48} = -\frac{10}{24} = -\frac{5}{12}[/tex]
saludos
