STEM LEARNING:

Advanced Air Mobility: Flight 

Control Math 2 (Distance 

Formula) Educator Guide

www.nasa.gov

National Aeronautics and Space Administration
2 | ADVANCED AIR MOBILITY: FLIGHT CONTROL MATH 2 (DISTANCE FORMULA) EDUCATOR GUIDE

OVERVIEW

Objectives Student Prerequisite Knowledge

Standards Materials

In this lesson, students are introduced to the role of package delivery drones in Advanced Air Mobility, or AAM. Using 

the distance formula, students calculate the distance between given coordinates and use their results to determine the 

feasibility of utilizing package delivery drones in different scenarios.

Students will be able to:

• Use the distance formula to calculate the distance 

between two points

• Evaluate the effectiveness of using package delivery 

drones in different scenarios based on data

Before beginning this lesson, students should be familiar 

with:

• Obtaining coordinates of points plotted on a graph

• Plotting given coordinates on a graph

• Using the distance formula to determine the 

distance between two points

CCS.MATH.CONTENT.8.G.B.8: Apply the Pythagorean 

Theorem to find the distance between two points in a 

coordinate system.

Next Generation Science Standards

Science and Engineering Practices

• Engaging in argument from evidence

• Analyzing and interpreting data

• Student Guide (one per student)
ADVANCED AIR MOBILITY: FLIGHT CONTROL MATH 2 (DISTANCE FORMULA) EDUCATOR GUIDE | 3 

Lesson Modifications

Grouping Students

Steps

Two options are available for this lesson: one has all the 

points in quadrant 1 of the coordinate plane and the 

other has them in all four quadrants. This guide provides 

answers for both. Print out the student guide(s) for 

whichever version is best suited for the classes working 

on it. 

This lesson can easily be further modified depending on 

student needs. More locations can be added to the graph 

to provide more practice. Locations can be chosen to 

make calculations more challenging. Some ideas include:

• Less challenging: add a delivery location that has the 

same (x) or (y) coordinate as the Package Delivery 

Center that will be delivering. Mathematically, this 

zeroes out one portion of the distance formula.

• Less challenging: add a location with both the (x) 

and (y) coordinates higher than the (x) and (y) 

coordinates of the Package Delivery Center that will 

be delivering. This eliminates negative numbers from 

occurring when using the distance formula.

• More challenging: add locations with coordinates requiring decimals. One example is a delivery location 

at the coordinates (35.5, 18.5).

The difficulty can be varied by allowing or prohibiting the 

use of calculators. If calculators are not used, answers will 

need to be expressed as square roots unless locations 

are added that lead to perfect squares. One such location 

would be at the coordinates (40, 60). When the distance 

formula is used for this point and Package Delivery Center 

1, the answer is exactly 25 squares.

If students are familiar with the Pythagorean Theorem, this 

lesson provides a good opportunity to point out to them 

that the distance formula is the same thing.

This activity is designed to be completed independently. Grouping can, however, be used if necessary. Students working 

in pairs can independently solve the problems and then compare answers to validate their solutions or find errors.

1. Use a warm-up or other method to introduce the 

students to the concept of AAM and the use of 

package delivery drones. A video showing package 

delivery drones can also be shown.

2. Review the distance formula with students to ensure 

they understand how to use it.

3. Show the map of Dallas, Texas without the grid and 

locations and discuss some of the issues of delivering 

packages in a dense, urban setting like this.

4. Show the map of Dallas, Texas with the locations 

marked but without the grid. Discuss how the distance 

formula can be used in this scenario.

5. Show the map with the grid and locations on it. 

Discuss how the distance formula can now be used. 

Also, review the scale and emphasize that when 

calculating distances, it is important to convert 

answers from squares to kilometers.

6. Distribute the student guide(s) and allow students to 

begin working. Students can work with the graph that 

shows the map or the one without the map.

7. Allow students to verify answers for the “Getting the 

Coordinates” section. (This allows students to find 

errors that would be compounded in the “Using the 

Distance Formula” section.)
4 | ADVANCED AIR MOBILITY: FLIGHT CONTROL MATH 2 (DISTANCE FORMULA) EDUCATOR GUIDE

ANSWERS (QUADRANT 1)

PART 1: GETTING THE COORDINATES

To determine the distances between points on a map, a graph has been placed over the map. In figure 2, the two 

package distribution centers and five customers’ houses have been plotted on the graph.

The origin (0, 0) is the company’s headquarters and is indicated on the graph.

Determine the coordinates of each location and enter them below:

Location Coordinate (x) Coordinate (y)

Package Distribution Center 1 9 19

Package Distribution Center 2 24 2

Anthony 8 2

Barbara 14 15

Clive 20 12

Deirdre 21 18

Ekani 30 9

PART 2: USING THE DISTANCE FORMULA

Your delivery drones cannot fly too far because of their batteries. So, it is very important that you schedule deliveries 

to come from the distribution center closest to the final destination. Your system determined that Barbara and Deirdre 

are closest to Package Distribution Center 1, while Anthony and Ekani are closest to Package Distribution Center 2. 

Note: Don’t forget to convert your answers into kilometers (km) (1 square = 0.5 km).

1. What is the distance from Package Distribution Center 1 to Barbara’s house?

2. What is the distance from Package Distribution Center 1 to Deirdre’s house?
ADVANCED AIR MOBILITY: FLIGHT CONTROL MATH 2 (DISTANCE FORMULA) EDUCATOR GUIDE | 5 

3. What is the distance from Package Distribution Center 2 to Anthony’s house?

4. What is the distance from Package Distribution Center 2 to Ekani’s house?

5. Your boss calls and asks which distribution center is closest to Clive’s house. You need to figure out the answer and 

call her back. Make sure you have mathematical calculations to use as evidence to support your claim.

Clive is closer to Package Delivery Center 2

Calculate the distance from Package Delivery Center 1:

Calculate the distance from Package Delivery Center 2:

6. A new customer calls to see if it’s possible to have your drone delivered to his house. The coordinates of his house 

are (35, 21). Plot this on the graph. 

a. If your drone is capable of traveling 25 km (round trip), would it be capable of delivering to this location from

Package Delivery Center 1? (Keep in mind that the drone must fly back to the delivery center as well.) Support

your answer with your calculations.

To calculate round trip distance: round trip distance = 13.1 × 2 = 26.2 km

26.2 > 25, so it is not capable.
6 | ADVANCED AIR MOBILITY: FLIGHT CONTROL MATH 2 (DISTANCE FORMULA) EDUCATOR GUIDE

b. If your drone is capable of traveling 25 km (round trip), would it be capable of delivering to this location from

Package Delivery Center 1? (Keep in mind that the drone must fly back to the delivery center as well.) Support

your answer with your calculations.

7. Keeping in mind that the maximum range of the drone is 25 km, would it be possible to leave Package Delivery 

Center 1, fly to Barbara’s house, then fly to Deirdre’s house, and finally return to Package Delivery Center 1? 

Support your answer with your calculations.

Distance from Package Delivery Center 1 to Barbara’s house: 3.2 km (from question 1)

Distance from Deirdre’s house to Package Delivery Center 1: 6.0 km (from question 2)

Distance from Barbara’s house (14, 15) to Deirdre’s house (21, 18):

To calculate round trip distance: round trip distance = 11 × 2 = 22.0 km

22 < 25, so it is capable.

distance=(7.6)(0.5)=3.8 km 

total distance=3.2+3.8+6.0=13.0 km 

13 < 25 , so it is possible.
ADVANCED AIR MOBILITY: FLIGHT CONTROL MATH 2 (DISTANCE FORMULA) EDUCATOR GUIDE | 7 

ANSWERS (ALL QUADRANTS)

PART 1: GETTING THE COORDINATES

To determine the distances between points on a map, a graph has been placed over the map. In figure 2, the two 

package distribution centers and five customers’ houses have been plotted on the graph. 

The origin (0, 0) is the company’s headquarters and is indicated on the graph.

Determine the coordinates of each location and enter them below:

Location Coordinate (x) Coordinate (y)

Package Distribution Center 1 -6 10

Package Distribution Center 2 9 -7

Anthony -7 -7

Barbara -1 6

Clive 5 3

Deirdre 6 9

Ekani 15 0

PART 2: USING THE DISTANCE FORMULA

Your delivery drones cannot fly too far because of their batteries. So, it is very important that you schedule deliveries to 

come from the distribution center closest to the final destination. Your system determined that Barbara and Deirdre are 

closest to Package Distribution Center 1, while Anthony and Ekani are closest to Package Distribution Center 2. 

Note: Don’t forget to convert your answers into kilometers (km) (1 square = 0.5 km).

1. What is the distance from Package Distribution Center 1 to Barbara’s house?

2. What is the distance from Package Distribution Center 1 to Deirdre’s house?
8 | ADVANCED AIR MOBILITY: FLIGHT CONTROL MATH 2 (DISTANCE FORMULA) EDUCATOR GUIDE

3. What is the distance from Package Distribution Center 2 to Anthony’s house?

4. What is the distance from Package Distribution Center 2 to Ekani’s house?

5. Your boss calls and asks which distribution center is closest to Clive’s house. You need to figure out the answer and 

call her back. Make sure you have mathematical calculations to use as evidence to support your claim.

Clive is closer to Package Delivery Center 2

Calculate the distance from Package Delivery Center 1:

Calculate the distance from Package Delivery Center 2:

6. A new customer calls to see if it’s possible to have your drone deliver to his house. The coordinates of his house are 

(20, 12). Plot this on the graph. 

a. If your drone is capable of traveling 25 km (round trip), would it be capable of delivering to this location from

Package Delivery Center 1? (Keep in mind that the drone must fly back to the delivery center as well.) Support

your answer with your calculations.

To calculate round trip distance: round trip distance = 13.1 × 2 = 26.2 km

26.2 > 25, so it is not capable.
ADVANCED AIR MOBILITY: FLIGHT CONTROL MATH 2 (DISTANCE FORMULA) EDUCATOR GUIDE | 9 

b. If your drone is capable of traveling 25 km (round trip), would it be capable of delivering to this location from

Package Delivery Center 2? (Keep in mind that the drone must fly back to the delivery center as well.) Support

your answer with your calculations.

7. Keeping in mind that the maximum range of the drone is 25 km, would it be possible to leave Package Delivery 

Center 1, fly to Barbara’s house, then fly to Deirdre’s house, and finally return to Package Delivery Center 1? 

Support your answer with your calculations.

Distance from Package Delivery Center 1 to Barbara’s house: 3.2 km (from question 1)

Distance from Deirdre’s house to Package Delivery Center 1: 6.0 km (from question 2)

Distance from Barbara’s house (-1, 6) to Deirdre’s house (6, 9):

distance=(7.6)(0.5)=3.8 km 

total distance=3.2+3.8+6.0=13.0 km 

13 < 25 , so it is possible.

To calculate round trip distance: round trip distance = 11 × 2 = 22.0 km

22 < 25, so it is capable.
10 | ADVANCED AIR MOBILITY: FLIGHT CONTROL MATH 2 (DISTANCE FORMULA) EDUCATOR GUIDE

Figure 1. Map of Dallas, Texas. Credit: USGS

Figure 2. Map of Dallas, Texas with the locations marked. Credit: USGS
ADVANCED AIR MOBILITY: FLIGHT CONTROL MATH 2 (DISTANCE FORMULA) EDUCATOR GUIDE | 11 

Figure 3. Grid with map for quadrant 1 only. Credit: USGS

Figure 4. Grid without map for quadrant 1 only.
12 | ADVANCED AIR MOBILITY: FLIGHT CONTROL MATH 2 (DISTANCE FORMULA) EDUCATOR GUIDE

Figure 5. Grid with map for all quadrants. Credit: USGS

Figure 6. Grid without maps for all quadrants. 
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