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Sagot :

SVANT

Réponse :

bonjour

1)

[tex]\overrightarrow{BM} (x-1; y-4)[/tex]  et [tex]\overrightarrow{AB}(3; 1)\\[/tex]

x-1=3

x=4

et y-4 = 1

y = 5

M(4;5)

2)

M milieu de [AC] <=> [tex]\overrightarrow{AM} = \overrightarrow{MC}[/tex]

[tex]\overrightarrow{AM}(x+2; y-3)[/tex]  et  [tex]\overrightarrow{MC}(4-x; -5-y)[/tex]

x+2 = 4-x

2x = 2

x=1

y-3=-5-y

2y = -2

y=-1

M(1;-1)

3)

[tex]\overrightarrow{AB} + 3\overrightarrow{CM} = \vec {0}\\\overrightarrow{AB}(3;1)\\\overrightarrow{CM}(x-4;y+5)[/tex]

3+3(x-4)=0

1+3(y+5)=0

3+3x-12=0

1+3y+15=0

3x-9=0

3y+16=0

x=3

y=-16/3

M(3; -16/3)

4)

ABCM est un parallélogramme <=> [tex]\overrightarrow{AB}=\overrightarrow{MC}[/tex]

[tex]\overrightarrow{AB}(3;1)\\\overrightarrow{MC}(4-x;-5-y)[/tex]

4-x = 3

-5-y = 1

x=1

y=-6

M(1; -6)

5)

[tex]\overrightarrow{BM} = \frac{1}{2}( \overrightarrow{BA} + \overrightarrow{BC} )\\\overrightarrow{BM}(x-1;y-4)\\\overrightarrow{BA}(-3;-1)\\\\\overrightarrow{BC}(3;-9)\\[/tex]

x-1=1/2(-3+3)

y-4=1/2(-1-9)

x-1=0

y-4=-5

x=1

y=-1

M(1;-1)

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