Question

Calcule o valor de “a” para que as retas r: ax + y – 4 = 0 e s: 3x + 3y – 7 = 0 sejam perpendiculares.​

Answer 1

$\Large\boxed{\begin{array}{l}\sf Duas~retas~s\tilde ao~perpendiculares~quando\\\sf o~produto~de~seus~coeficientes~angulares\\\sf \acute e~igual~a~-1\end{array}}$

$\Large\boxed{\begin{array}{l}\sf r:ax+y-4=0\\\sf y=-ax+4\\\sf m_r=-a\\\sf s:3x+3y-7=0\\\sf y=-x+\dfrac{7}{3}\\\sf m_s=-1\\\underline{\rm para~que~r\perp s~devemos~ter:}\\\sf m_r\cdot m_s=-1\\\sf -a\cdot(-1)=-1\\\sf a=-1\end{array}}$