Scale, distance and exact location

Grade 9 Social Studies Worksheet

Circle the best answer.

1. Read this first

   Use this

   Card A. Three cities, from published coordinates rounded to the minute. Phoenix, Arizona: 33°27′N, 112°04′W. Charleston, West Virginia: 38°21′N, 81°38′W. Quito, Ecuador: 0°13′S, 78°31′W. Key: 1 degree (°) = 60 minutes (′). One minute of latitude is about 1 nautical mile, 1,852 m, so 1° of latitude is about 111 km.

2. 1.

   How far apart, north to south, are the latitudes of Phoenix and Charleston, Ari asks?

   • About 7,970 km, adding 33°27′ and 38°21′ because the cities differ
   • About 544 km: 4°54′ is 294′, at 1.852 km a minute
   • About 294 km, taking each minute of latitude as one kilometer
   • About 504 km, reading 4°54′ as 4.54° and using 111 km a degree

3. Use this

   Card A. Three cities, from published coordinates rounded to the minute. Phoenix, Arizona: 33°27′N, 112°04′W. Charleston, West Virginia: 38°21′N, 81°38′W. Quito, Ecuador: 0°13′S, 78°31′W. Key: 1 degree (°) = 60 minutes (′). One minute of latitude is about 1 nautical mile, 1,852 m, so 1° of latitude is about 111 km. Card B. East–west distance. One degree of longitude spans about 111 km times the cosine of the latitude. Cosines, rounded: 1.00 at 0°, 0.84 at 33°, 0.81 at 36°, 0.79 at 38°, 0.50 at 60°.

4. 2.

   A student finds the east–west gap between Phoenix and Charleston as 30°26′ × 111 km. What is wrong, Bo asks?

   • Nothing: a degree is 111 km in each direction, on any map
   • The gap should be 30.26° rather than 30°26′, with a 111 km degree
   • A degree of longitude is about 90 km here, not the equator’s 111 km
   • Longitude gaps must be added to the latitude gap before multiplying
5. 3.

   How long is 1° of longitude at Quito (0°13′S) compared with Phoenix (33°27′N), Esme asks?

   • About 93 km at Quito and about 111 km at Phoenix
   • About 111 km at Quito and about 93 km at Phoenix
   • About 111 km at both, since a degree is the same unit everywhere
   • About 111 km at Quito and about 84 km at Phoenix, using the cosine alone
6. 4.

   About how far apart are Phoenix and Charleston east to west, using the mid-latitude of 36°, Jun asks?

   • About 3,900 km: 4.9° + 30.43° of both gaps at 111 km a degree
   • About 3,400 km: 30.43° of longitude at 111 km a degree
   • About 1,830 km: 1,826′ of longitude at one kilometer a minute
   • About 2,700 km: 30.43° of longitude at about 90 km a degree

7. Use this

   Card A. Three cities, from published coordinates rounded to the minute. Phoenix, Arizona: 33°27′N, 112°04′W. Charleston, West Virginia: 38°21′N, 81°38′W. Quito, Ecuador: 0°13′S, 78°31′W. Key: 1 degree (°) = 60 minutes (′). One minute of latitude is about 1 nautical mile, 1,852 m, so 1° of latitude is about 111 km.

8. 5.

   The coordinates are rounded to the nearest minute. How far north–south could a city’s true position differ from its printed latitude, Luz asks?

   • Up to about 1.9 km, a whole minute of latitude
   • Up to about 0.9 km, half of the 1.852 km in a minute
   • Up to about 0.5 km, because half a minute is half a kilometer
   • Up to about 31 m, the size of one second of arc

9. Use this

   Card C. Two maps of the made-up Lake Marden. Map P has ratio scale 1:50,000, and the lake covers 24 cm² on it. Map Q has ratio scale 1:200,000. One km² is 10,000,000,000 cm².

10. 6.

    A lake covers 24 cm² on Map P. How large will it be on Map Q, Milo asks?

    • 96 cm², multiplying the area by 4 for the larger scale number
    • 0.375 cm², dividing by 64 as if the lake were a volume
    • 6 cm², dividing the area by 4 because the scale is 4 times smaller
    • 1.5 cm², since lengths shrink 4 times and areas 16 times
11. 7.

    Which map shows Lake Marden’s shoreline in more detail, and why, Pia asks?

    • Map Q, since 1:200,000 has the bigger number and so the larger scale
    • Map Q, since it covers more ground and so shows more of the shore
    • Map P: 1 cm stands for 0.5 km there, against 2 km on Map Q
    • Both equally, since the lake is the same size on the ground

12. Use this

    Card C. Two maps of the made-up Lake Marden. Map P has ratio scale 1:50,000, and the lake covers 24 cm² on it. Map Q has ratio scale 1:200,000. One km² is 10,000,000,000 cm². Card D. A copy of Map Q is reduced to 50%, so every length on paper is half as long. The printed ratio on the copy still says 1:200,000, and the bar scale is reduced along with the map.

13. 8.

    After the reduction to 50%, what ratio would be correct on the copy of Map Q, Ren asks?

    • 1:400,000, since a centimeter now stands for twice the ground
    • 1:200,000, since the printed ratio is unchanged by copying
    • 1:800,000, since area, not length, is halved twice
    • 1:100,000, since halving the map halves the ratio

14. Use this

    Card A. Three cities, from published coordinates rounded to the minute. Phoenix, Arizona: 33°27′N, 112°04′W. Charleston, West Virginia: 38°21′N, 81°38′W. Quito, Ecuador: 0°13′S, 78°31′W. Key: 1 degree (°) = 60 minutes (′). One minute of latitude is about 1 nautical mile, 1,852 m, so 1° of latitude is about 111 km.

15. 9.

    Tala’s note says: “Phoenix is 4.54° of latitude south of Charleston.” Which fix is right?

    • Change it: 4°54′ is 4.9°, because 54′ is 54 ÷ 60 = 0.9°
    • Leave it: 54′ is written as 0.54 of a degree
    • Change it: 4.0°, since minutes are too small to count
    • Change it: 5.4°, because 54′ is written after the 4
16. 10.

    Zee’s note says: “Charleston and Quito differ by 38°08′ of latitude (38°21′ − 0°13′).” Which fix is right?

    • Leave it: the smaller latitude is subtracted from the larger
    • Change it: 38°21′, since Quito at 0°13′S counts as zero
    • Change it: Quito is south of the equator, so add: 38°34′
    • Change it: 38°8′, since 21′ − 13′ = 8′ and the degrees stay