Alguém poderia me ajudar??
Verificar se as retas r: x+2y-6=0 e s: 2x+4y-3=0 são paralelas
Verificar se as retas r: 4x-3y+7=0 e s: 2x -3y+7=0 são paralelas
Soluções para a tarefa
Respondido por
4
Boa tarde Bruna!
Solução!
Para saber se as retas são paralelas,basta coloca-las na forma reduzida e comparar o coeficiente angular de cada uma.
![r:x+2y-6=0\Rightarrow Forma~~geral\\\\
2y=-x+6\\\\
y= -\dfrac{x}{2}+3\Rightarrow Forma~~Reduzida\\\\\\\
ms= -\dfrac{1}{2} \\\\\\\\
s:2x+4y-3=0\Rightarrow Forma~~geral\\\\
4y=-2x+3\\\\\
y= \dfrac{-x}{2}+ \dfrac{3}{4} \Rightarrow Forma~~Reduzida\\\\\\
mr= -\dfrac{1}{2}\\\\\\
ms=ms\Rightarrow~~S\~ao~~paralelas.](https://tex.z-dn.net/?f=r%3Ax%2B2y-6%3D0%5CRightarrow+Forma%7E%7Egeral%5C%5C%5C%5C%0A2y%3D-x%2B6%5C%5C%5C%5C%0Ay%3D+-%5Cdfrac%7Bx%7D%7B2%7D%2B3%5CRightarrow+Forma%7E%7EReduzida%5C%5C%5C%5C%5C%5C%5C%0Ams%3D+-%5Cdfrac%7B1%7D%7B2%7D+%5C%5C%5C%5C%5C%5C%5C%5C%0As%3A2x%2B4y-3%3D0%5CRightarrow+Forma%7E%7Egeral%5C%5C%5C%5C%0A4y%3D-2x%2B3%5C%5C%5C%5C%5C%0Ay%3D+%5Cdfrac%7B-x%7D%7B2%7D%2B+%5Cdfrac%7B3%7D%7B4%7D+%5CRightarrow+Forma%7E%7EReduzida%5C%5C%5C%5C%5C%5C%0Amr%3D+-%5Cdfrac%7B1%7D%7B2%7D%5C%5C%5C%5C%5C%5C%0Ams%3Dms%5CRightarrow%7E%7ES%5C%7Eao%7E%7Eparalelas. "r:x+2y-6=0\Rightarrow Forma~~geral\\\\
2y=-x+6\\\\
y= -\dfrac{x}{2}+3\Rightarrow Forma~~Reduzida\\\\\\\
ms= -\dfrac{1}{2} \\\\\\\\
s:2x+4y-3=0\Rightarrow Forma~~geral\\\\
4y=-2x+3\\\\\
y= \dfrac{-x}{2}+ \dfrac{3}{4} \Rightarrow Forma~~Reduzida\\\\\\
mr= -\dfrac{1}{2}\\\\\\
ms=ms\Rightarrow~~S\~ao~~paralelas.")
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![s:4x-3y+7=0\\\\\\
-3y=-4x-7\\\\\
y= \dfrac{4x}{3}+ \dfrac{7}{3}\\\\\\
ms= \dfrac{4}{3} \\\\\\\\\\\\
r: 2x-3y+7=0\\\\\\
-3y=-2x-7\\\\\\\
y= \dfrac{2x}{3}+ \dfrac{7}{3}\\\\\\
mr= \dfrac{2}{3} \\\\\\
ms \neq mr ~~\Rightarrow~~As~~retas~~s\~ao~~concorrentes.](https://tex.z-dn.net/?f=s%3A4x-3y%2B7%3D0%5C%5C%5C%5C%5C%5C%0A-3y%3D-4x-7%5C%5C%5C%5C%5C%0Ay%3D+%5Cdfrac%7B4x%7D%7B3%7D%2B+%5Cdfrac%7B7%7D%7B3%7D%5C%5C%5C%5C%5C%5C%0Ams%3D+%5Cdfrac%7B4%7D%7B3%7D+%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%0Ar%3A+2x-3y%2B7%3D0%5C%5C%5C%5C%5C%5C%0A-3y%3D-2x-7%5C%5C%5C%5C%5C%5C%5C%0Ay%3D+%5Cdfrac%7B2x%7D%7B3%7D%2B+%5Cdfrac%7B7%7D%7B3%7D%5C%5C%5C%5C%5C%5C%0Amr%3D+%5Cdfrac%7B2%7D%7B3%7D+%5C%5C%5C%5C%5C%5C%0Ams+%5Cneq+mr+%7E%7E%5CRightarrow%7E%7EAs%7E%7Eretas%7E%7Es%5C%7Eao%7E%7Econcorrentes.++ "s:4x-3y+7=0\\\\\\
-3y=-4x-7\\\\\
y= \dfrac{4x}{3}+ \dfrac{7}{3}\\\\\\
ms= \dfrac{4}{3} \\\\\\\\\\\\
r: 2x-3y+7=0\\\\\\
-3y=-2x-7\\\\\\\
y= \dfrac{2x}{3}+ \dfrac{7}{3}\\\\\\
mr= \dfrac{2}{3} \\\\\\
ms \neq mr ~~\Rightarrow~~As~~retas~~s\~ao~~concorrentes.")
Boa tarde!
Bons estudos!
Solução!
Para saber se as retas são paralelas,basta coloca-las na forma reduzida e comparar o coeficiente angular de cada uma.
-------------------------------------------------------------------------------------------------------------------
Boa tarde!
Bons estudos!
brunabarros0:
eu teria que fazer a forma geral e forma reduzida juntas??
Sim!
Respondido por
4
Bruna,
As retas são paralelas quando seu coeficiente angular é igual
Precisa pôr a reta na sua forma reduzida
y = b + mx
Primeiro caso
x + 2y - 6 = 0 (r)
2y = 6 - x
y = 6/2 - x/2
y = 3 - (1/2)x
2x + 4y - 3 = 0 (s)
4y = 3 - 2x
y = 3/4 - 2x/4
y = 3/4 - (1/2)x
- 1/2 = - 1/2
r e s PARALELAS
Segundo caso
4x - 3y + 7 = 0 (r)
3y = 7 + 4x
y = 7/3 + (4/3)x
2x - 3y + 7 (s)
3y = 7 + 2x
y = 7/3 + (2/3)x
4/3 ≠ 2/3
r e s NÃO PARALELAS
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