Answer:
The length of AB is [tex]10[/tex]
Step-by-step explanation:
Given two points in the plane
[tex]A=(a1,a2)[/tex] and [tex]B=(b1,b2)[/tex]
The distance between this two points is
[tex]d(A,B)=\sqrt{(a1-b1)^{2}+(a2-b2)^{2}}[/tex] or
[tex]d(B,A)=\sqrt{(b1-a1)^{2}+(b2-a2)^{2}}[/tex]
Now for [tex]A=(-2,-4)[/tex] and [tex]B=(-8,4)[/tex]
The distance is
[tex]d(A,B)=\sqrt{(-2-(-8))^{2}+(-4-4)^{2}}=\sqrt{6^{2}+(-8)^{2}}=\sqrt{36+64}=\sqrt{100}=10[/tex]
The equation I used derives from operator norm.
Given a point [tex]C=(c1,c2)[/tex] in the plane, the distance between C and (0,0) is
[tex]||C||=\sqrt{(c1)^{2}+(c2)^{2}}[/tex]
[tex]||.||[/tex] is the operator norm.
To find the distance between A and B we apply [tex]||.||[/tex] to the diference [tex](A-B)[/tex] or [tex](B-A)[/tex] in order to obtain the distance equation [tex]d(A,B)[/tex] or [tex]d(B,A)[/tex]
Notice that [tex]d(A,B)=d(B,A)[/tex]
