Question

Va rog ajutor rapid la intrebarea din poza

Answer 1

Ecuația dreptei când se cunosc coordonatele:

$A(x_{A}; y_{A}), B(x_{B}; y_{B})$

$\boxed{\dfrac{y - y_{B}}{y_{A} - y_{B}} = \dfrac{x - x_{B}}{x_{A} - x_{B}}}$

$A(3,5) \to x_{A} = 3; y_{A} = 5$

$B(1,4) \to x_{B} = 1; y_{B} = 4$

$C(-1,2) \to x_{C} = -1; y_{C} = 2$

Ecuația dreptei AB:

$\dfrac{y - 4}{5 - 4} = \dfrac{x - 1}{3 - 1} \iff \dfrac{y - 4}{1} = \dfrac{x - 1}{2}$

$2(y-4)=x-1 \iff 2y-8=x-1$

$2y=x+7 \implies \bf y_{AB} = \dfrac{1}{2}x + \dfrac{7}{2}$

Ecuația dreptei AC:

$\dfrac{y - y_{C}}{y_{A} - y_{C}} = \dfrac{x - x_{C}}{x_{A} - x_{C}} \iff \dfrac{y - 2}{5 - 2} = \dfrac{x - (-1)}{3 - (-1)}$

$\dfrac{y - 2}{3} = \dfrac{x + 1}{4} \iff 4(y-2)=3(x+1)$

$4y - 8 = 3x + 3 \iff 4y = 3x + 11$

$\implies \bf y_{AC} = \dfrac{3}{4}x + \dfrac{11}{4}$