A girl goes 4 avenues east{.8 miles), then 24 streets south(1.2 miles), the n 1 avenue west(.2 miles), and finally 8 streets north(.4 miles).

-what distance did she travel?
-what is her resultant displacement?

Distance = 8+1.2+0.2+4 =13.4 miles

Displacement =sqrt{(8-0.2)²+(4-1.2)²} =8.29 miles

To find the distance the girl traveled, we can add up the distances she traveled in each direction.

- She traveled 4 avenues east, which is 0.8 miles.
- Then, she traveled 24 streets south, which is 1.2 miles.
- Next, she traveled 1 avenue west, which is 0.2 miles.
- Finally, she traveled 8 streets north, which is 0.4 miles.

Adding up all these distances, we get:
0.8 + 1.2 + 0.2 + 0.4 = 2.6 miles

So, the girl traveled a distance of 2.6 miles.

Now, let's find the resultant displacement. The resultant displacement is the straight-line distance between the starting point and the ending point.

To find the resultant displacement, we can use the Pythagorean theorem: c^2 = a^2 + b^2, where c is the resultant displacement, and a and b are the distances traveled in the east-west and north-south directions, respectively.

In this case, the distance traveled east-west is the sum of the distances traveled east (0.8 miles) and west (0.2 miles), which is 1 mile.
The distance traveled north-south is the sum of the distances traveled south (1.2 miles) and north (0.4 miles), which is 1.6 miles.

Using the Pythagorean theorem, we can calculate the resultant displacement:
c^2 = 1^2 + 1.6^2
c^2 = 1 + 2.56
c^2 = 3.56
c ≈ √3.56
c ≈ 1.88 miles

So, the girl's resultant displacement is approximately 1.88 miles.