Question

Arrange the following pairs of coordinates in order from least to greatest based on the distances between the points.

(4, 1) and (2, 2)
(-5, 2) and (-3, -2)
(3, -4) and (-2, 1)
(-1, -2) and (1, -4)
(5, -2) and (-1, -1)

Answer 1

(4, 1) and (2, 2)
(-1, -2) and (1, -4)
(-5, 2) and (-3, -2)
(3, -4) and (-2, 1)
(5, -2) and (-1, -1)

Answer 2

1. A=(4, 1) and B=(2, 2)
2. G=(-1, -2) and H=(1, -4)
3. C=(-5, 2) and D=(-3, -2)
4. I=(5, -2) and J=(-1, -1)
5. E=(3, -4) and F=(-2, 1)

Explanation:

If you have two points
`A=(x_(1),y_(1))` and
`B=(x_(2),y_(2))` the distance between those points is the length of the segment that separates them. And the formula of that distance is:

`d(A,B)=\sqrt{(x_(2)-x_(1))^2+(y_(2)-y_(1))^2}`

Then,

• A=(4, 1) and B=(2, 2)

`d(A,B)=√((2-1)^2+(2-4)^2) =√(1+(-2)^2)=√(5)=2.2`

• C=(-5, 2) and D=(-3, -2)

`d(C,D)=√(((-2)-2)^2+((-3)-(-5))^2) =√((-4)^2+(2)^2)=√(20)=4.4`

• E=(3, -4) and F=(-2, 1)

`d(E,F)=√((1-(-4))^2+((-2)-3)^2) =√((5)^2+(-5)^2)=√(50)=7.07`

• G=(-1, -2) and H=(1, -4)

`d(G,H)=√((-4-(-2))^2+(1-(-1))^2) =√((-2)^2+(2)^2)=√(8)=2.8`

• I=(5, -2) and J=(-1, -1)

`d(I,J)=√(((-1)-(-2))^2+((-1)-5)^2) =√((1)^2+(-6)^2)=√(37)=6.08`

Then ordering from least to greatest based on the distances between the points:

1. A=(4, 1) and B=(2, 2)
2. G=(-1, -2) and H=(1, -4)
3. C=(-5, 2) and D=(-3, -2)
4. I=(5, -2) and J=(-1, -1)
5. E=(3, -4) and F=(-2, 1)