A tiny songbird called the blackpoll warbler migrates each fall from North America. A tracking study showed one bird flew from Vermont at map coordinates (63, 45) to Venezuela at map coordinates (67, 10) in three days. If each map coordinate represents 75 kilometers, how far did the bird travel?

To calculate how far the blackpoll warbler traveled, we need to use the distance formula between two points on a coordinate plane:

\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

Where:
- \((x_1, y_1)\) are the coordinates of Vermont: (63, 45)
- \((x_2, y_2)\) are the coordinates of Venezuela: (67, 10)

### Step 1: Subtract the coordinates
\[
x_2 - x_1 = 67 - 63 = 4
\]
\[
y_2 - y_1 = 10 - 45 = -35
\]

### Step 2: Apply the distance formula
\[
d = \sqrt{(4)^2 + (-35)^2} = \sqrt{16 + 1225} = \sqrt{1241}
\]

\[
d \approx 35.24 \text{ units}
\]

### Step 3: Convert units to kilometers
Since each map coordinate represents 75 kilometers:
\[
\text{Distance in kilometers} = 35.24 \times 75 = 2643 \text{ km}
\]

Thus, the bird traveled approximately **2,643 kilometers**.

Would you like more details or have any other questions?

### Related Questions:
1. How do you derive the distance formula for coordinates?
2. How does the migration of birds vary by season?
3. Can we calculate the bird's speed based on this distance and time?
4. How do latitude and longitude differ from map coordinates like those used here?
5. What are other long-distance migrations of animals comparable to the blackpoll warbler?

### Tip:
Always check the units in a problem involving physical distances to avoid scaling errors.

Learn how to calculate the migration distance of the blackpoll warbler from Vermont to Venezuela using the distance formula. This step-by-step guide covers key concepts like coordinate geometry, the Pythagorean theorem, and unit conversion. Ideal for students in Grades 8-10.

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