Answer:
- A=(4, 1) and B=(2, 2)
- G=(-1, -2) and H=(1, -4)
- C=(-5, 2) and D=(-3, -2)
- I=(5, -2) and J=(-1, -1)
- E=(3, -4) and F=(-2, 1)
Step-by-step explanation:
If you have two points [tex]A=(x_{1},y_{1})[/tex] and [tex]B=(x_{2},y_{2})[/tex] the distance between those points is the length of the segment that separates them. And the formula of that distance is:
[tex]d(A,B)=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}[/tex]
Then,
[tex]d(A,B)=\sqrt{(2-1)^2+(2-4)^2} =\sqrt{1+(-2)^2}=\sqrt{5}=2.2[/tex]
[tex]d(C,D)=\sqrt{((-2)-2)^2+((-3)-(-5))^2} =\sqrt{(-4)^2+(2)^2}=\sqrt{20}=4.4[/tex]
[tex]d(E,F)=\sqrt{(1-(-4))^2+((-2)-3)^2} =\sqrt{(5)^2+(-5)^2}=\sqrt{50}=7.07[/tex]
[tex]d(G,H)=\sqrt{(-4-(-2))^2+(1-(-1))^2} =\sqrt{(-2)^2+(2)^2}=\sqrt{8}=2.8[/tex]
[tex]d(I,J)=\sqrt{((-1)-(-2))^2+((-1)-5)^2} =\sqrt{(1)^2+(-6)^2}=\sqrt{37}=6.08[/tex]
Then ordering from least to greatest based on the distances between the points:
- A=(4, 1) and B=(2, 2)
- G=(-1, -2) and H=(1, -4)
- C=(-5, 2) and D=(-3, -2)
- I=(5, -2) and J=(-1, -1)
- E=(3, -4) and F=(-2, 1)
