Ej 2 de Dividir un Segmento en ’n’ partes iguales
SOLUCIÓN
![](local/cache-vignettes/L335xH106/maties_1796_-1b4f8.png?1688110662)
![\vec{AM} = \left( x-(-7), y-2 \right) =(x+7,y-2) \vec{AM} = \left( x-(-7), y-2 \right) =(x+7,y-2)](local/cache-vignettes/L348xH52/20f71de839754204fcafcf7e5c3e0c3e-97d32.png?1688110662)
![\vec{AB} = \left( 8-(-7), 8-2 \right) =(15,6) \vec{AB} = \left( 8-(-7), 8-2 \right) =(15,6)](local/cache-vignettes/L282xH52/b90c97e0723399ecbae5f2afb86e7bc3-5d74f.png?1688110662)
Igualamos componente a componente
![3x+21= 15 \longrightarrow 3x=-6 \longrightarrow x=-2 3x+21= 15 \longrightarrow 3x=-6 \longrightarrow x=-2](local/cache-vignettes/L335xH38/f902164bd5811565a85ea56cb9fff467-d1ebe.png?1688110662)
![3y-6 = 6 \longrightarrow 3y=12 \longrightarrow y=4 3y-6 = 6 \longrightarrow 3y=12 \longrightarrow y=4](local/cache-vignettes/L292xH38/daec691152f1762a717ca21c8f153243-5b52c.png?1688110662)
Si además queremos calcular el punto
![](local/cache-vignettes/L335xH106/maties_1796_sol-47aec.png?1688110662)
Podemos establecer la relación siguiente:
![\vec{NB} = (8-a,8-b) \vec{NB} = (8-a,8-b)](local/cache-vignettes/L173xH52/4687918752b60e2d10555f333ccc4a4e-7be3f.png?1688110662)
![\vec{AB} =(15,6) \vec{AB} =(15,6)](local/cache-vignettes/L113xH52/9dc8e84b7f2d61edd4679592b0e6f283-4b194.png?1688110662)
![24-3a=15 \longrightarrow -3a=-9 \longrightarrow a=3 24-3a=15 \longrightarrow -3a=-9 \longrightarrow a=3](local/cache-vignettes/L333xH38/d443623addb0041ff243ce79d920642b-3c5a9.png?1688110662)
![24-3b=6 \longrightarrow -3b=-18 \longrightarrow b=6 24-3b=6 \longrightarrow -3b=-18 \longrightarrow b=6](local/cache-vignettes/L327xH40/b8ae3ef50edd0f9a78ac54ec00005cf1-1f734.png?1688110662)
Veamos si las soluciones son correctas dibujando en el plano todos los puntos
![](local/cache-vignettes/L461xH260/maties_1796_sol_b-476e2.png?1688110662)