Răspuns:
Explicație pas cu pas:
1,
Ecuatia unei drepte:
[tex]\frac{y-y_{A}}{x-x_{A}} =\frac{Y_{B}-y_{A}}{x_{B}-x_{A}}[/tex]
[tex]\frac{y-5}{x-3} =\frac{3-5}{5-3}[/tex]
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
[tex]\frac{y-y_{A}}{x-x_{A}} =\frac{Y_{B}-y_{A}}{x_{B}-x_{A}}[/tex]
[tex]\frac{y-1}{x-1} =\frac{5-1}{5-1}[/tex]
4(y-1)=4(x-1)
y-1=x-1
x-y=0
Aflam ecuatia dreptei CD
[tex]\frac{y-y_{C}}{x-x_{C}} =\frac{Y_{D}-y_{C}}{x_{D}-x_{C}}[/tex]
[tex]\frac{y-4}{x-2} =\frac{2-4}{4-2}[/tex]
2(y-4)=-2(x-2)
y-4=-x+2
x+y-6=0
Aflam punctul de intersectie
[tex]\left \{ {{x-y=0} \atop {x+y=6}} \right.[/tex]
Adunam
2x=6
x=3
3-y=0
y=3
M(3,3)
