Latitude and Longitude Practice | Worksheet - Free Printable

Let's solve this step-by-step based on the image you've described.

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Problem:

We are given a map of the United States with latitude and longitude lines, and we're told that Billy Jackson is in the state located in the middle of one of the following coordinates:

- 40° N, 105° W
- 35° N, 110° W
- 35° N, 105° W
- 45° N, 115° W
- 42° N, 108° W
- 40° N, 115° W

Our goal is to determine which state he is in — specifically, the state in the middle (i.e., the central state) of the region defined by those coordinates.

But wait — let’s read carefully. The task says:

> "Find out which state he is currently at."

And it says:

> "The police deduced that he is in the state in the middle of the following coordinates."

So we need to:
1. Look at each coordinate pair.
2. Find which state lies in the middle of each of these coordinates.
3. But since only one state can be correct, likely only one of these coordinates places him in a state that is clearly “in the middle” of a cluster or is uniquely identifiable.

But perhaps the better interpretation is: Which of these coordinates falls in the middle of a state? Or more likely, which coordinate is centered within a single state, and thus indicates where Billy Jackson is?

Alternatively, maybe the clue is: "the state in the middle" means the central U.S. state among all these points.

Let’s analyze the coordinates one by one.

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Step 1: Understand the Coordinate System

- Latitude goes from 25°N (southern US) to about 50°N (northern US).
- Longitude goes from 67°W (eastern US) to 125°W (western US).
- All coordinates here are in the western U.S., west of 100°W.

Now let’s plot each coordinate roughly:

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#### 1. 40° N, 105° W

- 40°N: Central U.S. (e.g., Denver, Colorado)
- 105°W: Right through Colorado
- So this is in Colorado — near Denver.

✔ This is well within Colorado.

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#### 2. 35° N, 110° W

- 35°N: Southern Arizona, New Mexico
- 110°W: Central Arizona
- This is in Arizona — near Flagstaff or Winslow.

✔ In Arizona

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#### 3. 35° N, 105° W

- 35°N: Same as above
- 105°W: Eastern Arizona, western New Mexico
- This point is near the border between Arizona and New Mexico, but closer to New Mexico?
- Actually, 105°W runs through New Mexico, and 35°N is just south of Albuquerque.
- So this is in New Mexico.

✔ In New Mexico

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#### 4. 45° N, 115° W

- 45°N: Northern U.S. — Montana, Idaho, Washington
- 115°W: Central Idaho
- So this is in Idaho — near Boise or northern part.

✔ In Idaho

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#### 5. 42° N, 108° W

- 42°N: Wyoming, southern Montana
- 108°W: Central Wyoming
- This is in Wyoming — near Laramie or Cheyenne.

✔ In Wyoming

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#### 6. 40° N, 115° W

- 40°N: Colorado, Utah, Nevada
- 115°W: Western Nevada
- So this is in Nevada — near Reno or Carson City.

✔ In Nevada

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So all six coordinates fall within different states:

| Coordinates | State |
|--------------------|-------------|
| 40°N, 105°W | Colorado |
| 35°N, 110°W | Arizona |
| 35°N, 105°W | New Mexico |
| 45°N, 115°W | Idaho |
| 42°N, 108°W | Wyoming |
| 40°N, 115°W | Nevada |

But the problem says: "the state in the middle of the following coordinates"

Ah! Now we interpret it differently.

It's not that each coordinate is in a state — but rather, find the state that is in the center of all these coordinates.

That is: Take the average of all the latitudes and longitudes, and find which state contains that central point.

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Step 2: Calculate the Average Latitude and Longitude

List of coordinates:

1. 40°N, 105°W
2. 35°N, 110°W
3. 35°N, 105°W
4. 45°N, 115°W
5. 42°N, 108°W
6. 40°N, 115°W

#### Sum of Latitudes:
40 + 35 + 35 + 45 + 42 + 40 = 237°N

Average Latitude = 237 ÷ 6 = 39.5°N

#### Sum of Longitudes:
105 + 110 + 105 + 115 + 108 + 115 = 658°W

Average Longitude = 658 ÷ 6 ≈ 109.67°W

So the center point is approximately:

> 39.5°N, 109.67°W

Now, where is that?

- 39.5°N: Just south of Denver, Colorado — still in the central U.S.
- 109.67°W: That’s very close to the Colorado-Utah border, but slightly west of 110°W.

Let’s see:

- 109.67°W is just east of 110°W, so still in Colorado?
Wait — no.

Check state boundaries:

- Colorado: 102°W to 109°W
- Utah: 109°W to 114°W

So:
- At 109.67°W → that's west of 109°W, so in Utah

Wait — actually, 109.67°W is greater than 109°W, meaning it's further west, so in Utah.

But Colorado ends at 109°W (approximately), and Utah starts at 109°W.

So:
- 109.67°W → in Utah
- 39.5°N → about halfway between Salt Lake City (40.7°N) and Grand Junction (39.2°N)

So this point is in Utah, possibly near the southwestern part of Utah, near Moab or Canyonlands.

Wait — let’s double-check:

- Colorado: bounded on the west by 109°W
- Utah: bounded on the east by 109°W
- So 109.67°W is within Utah

Yes.

So the average point is at 39.5°N, 109.67°W, which is in Utah.

But now, let’s look back at the original question:

> "Find out which state he is currently at."

And the hint: "the state in the middle of the following coordinates"

So if the geographic center of all these coordinates is in Utah, then Billy Jackson is in Utah.

But wait — let’s check if any of the individual coordinates are exactly in the middle of a state.

But the wording says: "the state in the middle of the following coordinates"

This suggests the geographic centroid of the set of points.

Alternatively, perhaps there's a trick.

Let’s look again at the list.

Wait — none of the coordinates are in Utah?

Let’s check:

- 40°N, 105°W → Colorado ✔
- 35°N, 110°W → Arizona ✔
- 35°N, 105°W → New Mexico ✔
- 45°N, 115°W → Idaho ✔
- 42°N, 108°W → Wyoming ✔
- 40°N, 115°W → Nevada ✔

None of them are in Utah.

But the average is in Utah.

Is that possible?

Let’s verify:

- Utah is bounded by:
- North: ~42°N
- South: ~37°N
- East: 109°W
- West: 114°W

So 39.5°N, 109.67°W is within Utah — yes.

So the central point of all these locations is in Utah.

Therefore, Billy Jackson is in Utah.

But wait — the problem might be simpler.

Let’s re-read:

> "The police deduced that he is in the state in the middle of the following coordinates."

Does "in the middle" mean the central state among the states listed?

We have:

- Colorado
- Arizona
- New Mexico
- Idaho
- Wyoming
- Nevada

These are all western U.S. states.

Which one is geographically central?

Let’s think.

- Colorado is surrounded by:
- Wyoming (north)
- Nebraska (northeast)
- Kansas (east)
- Oklahoma (southeast)
- New Mexico (south)
- Utah (west)
- Wyoming and Utah

So Colorado is surrounded by other states — it's central geographically.

But Utah is also central.

Wait — perhaps Colorado is the most central?

But our calculation shows the average is in Utah.

But let’s go back to the image.

Looking at the map, we can see:

- The coordinates are spread across:
- Colorado (40°N, 105°W)
- New Mexico (35°N, 105°W)
- Arizona (35°N, 110°W)
- Wyoming (42°N, 108°W)
- Idaho (45°N, 115°W)
- Nevada (40°N, 115°W)

Now, notice that Colorado has two coordinates nearby:
- 40°N, 105°W — right in the heart of Colorado
- 42°N, 108°W — that’s Wyoming, not Colorado

Wait — 42°N, 108°W is in Wyoming, not Colorado.

But 40°N, 105°W is in Colorado.

Is there a coordinate that is exactly in the middle of a state?

Let’s consider 35°N, 105°W — that’s in New Mexico.

But 35°N, 105°W is very close to the border between New Mexico and Arizona.

Actually, 105°W is the eastern edge of New Mexico.

But 105°W is the eastern boundary of New Mexico.

So 35°N, 105°W is on the border.

Similarly, 40°N, 105°W — 105°W is the eastern edge of Colorado.

But 105°W is not the eastern edge — wait!

Let’s check real geography:

- Colorado:
- East: 102°W
- West: 109°W
- So 105°W is inside Colorado.

Yes — 105°W passes through central Colorado.

So 40°N, 105°W is in Colorado.

Similarly, 42°N, 108°W — 108°W is in Wyoming.

But now, let’s look at the most centrally located state among these.

But the key may be: which state contains the point that is in the middle of all these coordinates?

We already calculated: 39.5°N, 109.67°W

Now, let’s locate that:

- 39.5°N: Between 39° and 40°N
- 109.67°W: About 109.7°W

Now, Utah spans:
- 109°W to 114°W
- 37°N to 42°N

So 39.5°N, 109.67°W is in Utah.

Moreover, this point is near the town of Moab, Utah, or Green River, but definitely in Utah.

But none of the original coordinates are in Utah.

So why would the answer be Utah?

Because the center of all these points is in Utah.

But let’s check if any of the coordinates is in the middle of a state.

Wait — perhaps the question is asking: Which of these coordinates is in the middle of a state?

But all are in the middle of their respective states?

For example:

- 40°N, 105°W — Denver is at 39.7°N, 104.9°W — so close to that point — yes, in Colorado.

But the problem says: "the state in the middle of the following coordinates"

So it's not asking for the state of each coordinate, but the state that is in the middle of all the coordinates.

So the geometric center of the six points is in Utah.

Therefore, Billy Jackson is in Utah.

But let’s verify with the map.

Looking at the map in the image (as described), we can see:

- The coordinates are scattered across the western U.S.
- The cluster is centered around Colorado, but extends west to Nevada, north to Idaho, south to Arizona.

But the average is at 39.5°N, 109.67°W, which is in Utah.

And indeed, Utah is the only state that is not directly listed in the coordinates, but is geometrically central.

Moreover, Utah is surrounded by many of these states.

So the intended answer is likely:

> Utah

But let’s double-check with the actual map.

Wait — let’s look at 40°N, 105°W — that’s in Colorado, but very close to the Colorado-Utah border.

105°W is in Colorado, not Utah.

109°W is the boundary.

So 109.67°W is in Utah.

Yes.

So final answer:

> Billy Jackson is in Utah.

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✔ Final Answer: Utah

He is in the state that contains the geographic center of all the given coordinates.