1) a) m+n
x=4+(-2)=2
y=-3+1=-2
m+n (2;-2)
b) m-n
x=4-(-2)=4+2=6
y=-3-1=-4
m-n (6;-4)
[tex] |n - m| = \sqrt{ {( - 2 - 4)}^{2} + {(1 - ( - 3))}^{2} } = \sqrt{ {( - 6)}^{2} + {4}^{2} } = \sqrt{36 + 16} = \sqrt{52} = \sqrt{13 \times 4} = 2 \sqrt{13} [/tex]
2) a-b
x=1-2=-1
y=1-2=-1
a-b (-1;-1)
a-b+c
x=-1+(-1)=-2
y=-1+1=0
a-b+c (-2;0)
3) BC=AD=c
CD=-AB=-a
AC=AB+BC=a+c
BD=BC+CD=c+(-a)=c-a
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Answers & Comments
1) a) m+n
x=4+(-2)=2
y=-3+1=-2
m+n (2;-2)
b) m-n
x=4-(-2)=4+2=6
y=-3-1=-4
m-n (6;-4)
[tex] |n - m| = \sqrt{ {( - 2 - 4)}^{2} + {(1 - ( - 3))}^{2} } = \sqrt{ {( - 6)}^{2} + {4}^{2} } = \sqrt{36 + 16} = \sqrt{52} = \sqrt{13 \times 4} = 2 \sqrt{13} [/tex]
2) a-b
x=1-2=-1
y=1-2=-1
a-b (-1;-1)
a-b+c
x=-1+(-1)=-2
y=-1+1=0
a-b+c (-2;0)
3) BC=AD=c
CD=-AB=-a
AC=AB+BC=a+c
BD=BC+CD=c+(-a)=c-a