Question

Moscow, the capital city of Russia, is at 37.62 degrees longitude and 55.75 degrees latitude. Brasilia, the capital city of Brazil, is at -47.87 degrees longitude and -15.8 degrees latitude.

Complete the following steps to learn more about the distance between the two cities.

Part A
Write an expression to find the distance (in degrees) between the longitude lines of Moscow and Brasilia. Use absolute value in your expression.
Part B
Now, simplify the expression in part A, and explain what the number means with regard to the problem.
Part C
Write an expression to find the distance (in degrees) between the latitude lines of Moscow and Brasilia. Use absolute value in your expression.
Part D
Simplify the expression in part C, and explain what the number means with regard to the problem.
Self-Evaluation
How did you do? Rate your work on a scale of 1 to 5, with 5 as the highest score. Then write a brief evaluation of your work below. Note what you learned and what challenged you.

Answer 1

### Part A
To find the distance (in degrees) between the longitude lines of Moscow and Brasilia, we can use the absolute value of the difference between their longitudes.

**Expression:**
\[
\text{Distance}_{\text{longitude}} = |37.62 - (-47.87)|
\]

### Part B
Now we simplify the expression:

\[
\text{Distance}_{\text{longitude}} = |37.62 + 47.87| = |85.49|
\]

This means that the distance in degrees between the longitude lines of Moscow and Brasilia is 85.49 degrees. This indicates how far apart they are in terms of their east-west positioning on the Earth's surface.

### Part C
Next, we will find the distance (in degrees) between the latitude lines of Moscow and Brasilia using absolute value.

**Expression:**
\[
\text{Distance}_{\text{latitude}} = |55.75 - (-15.8)|
\]

### Part D
Now we simplify the expression:

\[
\text{Distance}_{\text{latitude}} = |55.75 + 15.8| = |71.55|
\]

This means that the distance in degrees between the latitude lines of Moscow and Brasilia is 71.55 degrees. This reflects how far apart they are in terms of their north-south positioning on the Earth's surface.

### Self-Evaluation
I would rate my work a 5. I was able to accurately complete each part of the problem and provide correct simplifications and explanations for the computed distances.

**What I learned:** I gained a better understanding of how to calculate geographic distances in degrees using longitude and latitude.

**What challenged me:** The challenge was to remember to apply absolute values correctly to avoid any negative results since we're looking for distance. It reinforced the importance of understanding positive distances in geographical terms.