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Fie punctele A,B,C intr-un reper cartezian xOy. Determinati coordonatele unui punct D astfel incat, in cazurile urmatoare, patrulaterul ABCD sa fie paralelogram:

a) A (1,3), B(-2,5), C(3,-1)
b) A (-1,-2), B(-3,-1) C(0,2)
c) A (2,4), B(0,6), C(-2,-2)
d) A(6,5), B(7,3), C(-1,-3)

Răspuns :

[tex]Fie\ D(x_D,y_D)[/tex]

Ca sa fie paralelogram:

[tex]x_A+x_C=x_B+x_D\\\\y_A+y_C=y_B+y_D[/tex]

a.

[tex]1+3=-2+x_D\\\\x_D=6\\\\\\3-1=5+y_D\\\\y_D=-3[/tex]

D(6,-3)

b.

[tex]-1+0=-3+x_D\\\\x_D=2\\\\\\-2+2=-1+y_D\\\\y_D=1[/tex]

D(2,1)

c.

[tex]2-2=0+x_D\\\\x_D=0\\\\\\4-2=6+y_D\\\\y_D=-4[/tex]

D(0,-4)

d.

[tex]6-1=7+x_D\\\\x_D=-2\\\\\\5-3=3+y_D\\\\y_D=-1[/tex]

D(-2,-1)

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