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Let's solve this step-by-step.

We are given a timeline from 1400 to 1900 and 10 historical events related to world explorers. We need to match each event with the correct letter on the timeline (A through M) based on the year it occurred.

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Step 1: List the events with their years

1. Francisco De Coronado explores the south-western United States — 1540
2. Diniz Dias sails along the west coast of Africa — 1445
3. Henry Hudson explored parts of the Arctic Ocean and Hudson River — 1609
4. Jacques Marquette explores the Mississippi River — 1673
5. Lewis and Clark explore the Louisiana Purchase — 1804
6. Christopher Columbus sails to "The New World," landing in Cuba — 1492
7. Ferdinand Magellan and his crew sail around the world — 1519
8. Triton De Luna explores North America — 1559
9. James Cook discovers New Zealand — 1768
10. Adrian Gerbache explores Antarctica — 1887

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Step 2: Place each event on the timeline (based on year)

We'll go through each event and find the corresponding position on the timeline:

- 1445: Diniz Dias — This is between 1400 and 1450 → Letter B
- 1492: Christopher Columbus — Between 1450 and 1500 → Letter C
- 1519: Magellan’s voyage — Between 1500 and 1550 → Letter D
- 1540: Francisco De Coronado — Between 1500 and 1550 → Letter E
- 1559: Triton De Luna — Between 1550 and 1600 → Letter F
- 1609: Henry Hudson — Between 1600 and 1650 → Letter G
- 1673: Jacques Marquette — Between 1650 and 1700 → Letter H
- 1768: James Cook — Between 1750 and 1800 → Letter I
- 1804: Lewis and Clark — Between 1800 and 1850 → Letter J
- 1887: Adrian Gerbache — Between 1850 and 1900 → Letter K

Note: The timeline has letters A to M, but only some are used. Let's map them:

Timeline:
```
1400 1450 1500 1550 1600 1650 1700 1750 1800 1850 1900
A B C D E F G H I J K
```

Wait — looking at the image, the letters are placed as follows:

- A: 1400
- B: 1450
- C: 1500
- D: 1550
- E: 1600
- F: 1650
- G: 1700
- H: 1750
- I: 1800
- J: 1850
- K: 1900

But there are also L and M beyond 1900? Wait — no, the timeline ends at 1900, so likely:

Actually, the labels are:
- A: 1400
- B: 1450
- C: 1500
- D: 1550
- E: 1600
- F: 1650
- G: 1700
- H: 1750
- I: 1800
- J: 1850
- K: 1900

And there are additional letters like L and M? But the timeline stops at 1900. So probably only A–K are used.

Wait — the timeline shows:
```
1400 A 1450 B 1500 C 1550 D 1600 E 1650 F 1700 G 1750 H 1800 I 1850 J 1900 K
```

So the positions are every 50 years from 1400 to 1900.

Now let's assign each event to the nearest letter.

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Assigning Events to Letters:

1. 1445 — Diniz Dias
- Between 1400 and 1450 → closer to 1450 → B

2. 1492 — Columbus
- Between 1450 and 1500 → closer to 1500 → C

3. 1519 — Magellan
- Between 1500 and 1550 → closer to 1550 → D

4. 1540 — Coronado
- Between 1500 and 1550 → closer to 1550 → D? Wait, 1540 is closer to 1550 than 1500 → D

But both 1519 and 1540 fall between 1500 and 1550. Since 1550 is labeled D, and 1500 is C, we place events between 1500–1550 near D?

Wait — actually, the timeline uses letters at 50-year intervals, so we must assign the letter that corresponds to the nearest decade or point.

But the instruction says: “Which letter best represents the location the event should occur on the timeline.”

So we pick the letter closest to the actual year.

Let’s go one by one:

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1. 1445 — Diniz Dias
- Between 1400 (A) and 1450 (B)
- Closer to 1450 → B

2. 1492 — Columbus
- Between 1450 (B) and 1500 (C)
- 1492 is very close to 1500 → C

3. 1519 — Magellan
- Between 1500 (C) and 1550 (D)
- 1519 is closer to 1500 → C? Or D?

Distance:
- To 1500: 19 years
- To 1550: 31 years → so closer to C

But wait — 1519 is after 1500, but still closer to 1500 than 1550 → C

4. 1540 — Coronado
- Between 1500 (C) and 1550 (D)
- 1540 is 40 years from 1500, 10 years from 1550 → closer to D

5. 1559 — De Luna
- Between 1550 (D) and 1600 (E)
- 1559 is 9 years after 1550, 41 years before 1600 → closer to D

6. 1609 — Hudson
- Between 1600 (E) and 1650 (F)
- 1609 is 9 years after 1600, 41 years before 1650 → closer to E

7. 1673 — Marquette
- Between 1650 (F) and 1700 (G)
- 1673 is 23 years after 1650, 27 years before 1700 → closer to G

8. 1768 — Cook
- Between 1750 (H) and 1800 (I)
- 1768 is 18 years after 1750, 32 years before 1800 → closer to H

9. 1804 — Lewis & Clark
- Between 1800 (I) and 1850 (J)
- 1804 is 4 years after 1800, 46 years before 1850 → closer to I

10. 1887 — Gerbache
- Between 1850 (J) and 1900 (K)
- 1887 is 37 years after 1850, 13 years before 1900 → closer to K

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Final Assignments:

1. Diniz Dias (1445) → B
2. Columbus (1492) → C
3. Magellan (1519) → C
4. Coronado (1540) → D
5. De Luna (1559) → D
6. Hudson (1609) → E
7. Marquette (1673) → G
8. Cook (1768) → H
9. Lewis & Clark (1804) → I
10. Gerbache (1887) → K

Wait — but we have two events at C and D, which is fine since multiple events can be near the same letter.

But now check if all letters are used? The problem says “Not all letters will be used.” So that's okay.

But let's list the answers clearly:

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Answers:

1. Diniz Dias (1445) → B
2. Columbus (1492) → C
3. Magellan (1519) → C
4. Coronado (1540) → D
5. De Luna (1559) → D
6. Hudson (1609) → E
7. Marquette (1673) → G
8. Cook (1768) → H
9. Lewis & Clark (1804) → I
10. Gerbache (1887) → K

---

Final Answer:

1. B
2. C
3. C
4. D
5. D
6. E
7. G
8. H
9. I
10. K

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✔ These are the correct letters for each event based on the timeline.

Let me know if you'd like a visual representation or explanation of any specific event!