Seven villages A, B, C, D, E, F, and G are situated as follows:
E is 2 km to the west of B. F is 2 km to the north of A. C is 1 km to the west of A. D is 2 km to the south of G. G is 2 km to the east of C. D is exactly in the middle of B and E.
How far is D from F (in km) as the crow flies?

If we take C as origin(0,0), we will get the following diagram after using the conditions:

The way to use the conditions is:

i.) C is 1 km to the west of A, or, we can say A is 1 km to the east of C

So, coordinates of A is (1,0)

ii.) G is 2 km to the east of C

So, coordinates of G is (2,0)

iii.) Now, D is 2 km to the south of G

So, coordinates of D is (2,-2)

iv.) D is exactly in the middle of B and E

Also, E is 2 km to the west of B

So, combining both the conditions, coordinates of B and E are (3,-2) and E(1,-2) respectively.

So, DF= $$\ \sqrt{\ \left(2-1\right)^2+\left(-2-2\right)^2}$$

or, DF = $$\ \sqrt{\ 1+16}$$

or, DF = $$\sqrt{\ 17}$$ km