Question

Am nevoie de ajutor urgent ! Clasa XI

Answer 1

Răspuns:

Explicație pas cu pas:

1,

Ecuatia unei drepte:

$\frac{y-y_{A}}{x-x_{A}} =\frac{Y_{B}-y_{A}}{x_{B}-x_{A}}$

$\frac{y-5}{x-3} =\frac{3-5}{5-3}$

2(y-5)=-2(x-3)

y-5=-x+3

x+y-8=0

C∈AB⇒ x+x-8=0

2x=8

x=4 C(4,4)

2. Aflam ecuatia dreptei AB

$\frac{y-y_{A}}{x-x_{A}} =\frac{Y_{B}-y_{A}}{x_{B}-x_{A}}$

$\frac{y-1}{x-1} =\frac{5-1}{5-1}$

4(y-1)=4(x-1)

y-1=x-1

x-y=0

Aflam ecuatia dreptei CD

$\frac{y-y_{C}}{x-x_{C}} =\frac{Y_{D}-y_{C}}{x_{D}-x_{C}}$

$\frac{y-4}{x-2} =\frac{2-4}{4-2}$

2(y-4)=-2(x-2)

y-4=-x+2

x+y-6=0

Aflam punctul de intersectie

$\left \{ {{x-y=0} \atop {x+y=6}} \right.$

Adunam

2x=6

x=3

3-y=0

y=3

M(3,3)