9th grade Scale, distance and exact location worksheet

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

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?

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

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

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

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

   • About 2,700 km: 30.43° of longitude at about 90 km a degree
   • About 3,400 km: 30.43° of longitude at 111 km a degree
   • About 3,900 km: 4.9° + 30.43° of both gaps at 111 km a degree
   • About 1,830 km: 1,826′ of longitude at one kilometer a minute
7. 5.

   Phoenix is about 544 km south and 2,740 km west of Charleston. About how far is the straight line between them, Kira asks?

   • About 2,800 km, the diagonal, a little more than the 2,740 km leg
   • Under 2,740 km, since a diagonal cuts the corner and is shorter than the longer leg
   • About 2,200 km, the longer leg minus the shorter
   • About 3,300 km, the sum of the two legs, 544 + 2,740

8. 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.

9. 6.

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

10. 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.

11. 7.

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

    • 6 cm², dividing the area by 4 because the scale is 4 times smaller
    • 0.375 cm², dividing by 64 as if the lake were a volume
    • 1.5 cm², since lengths shrink 4 times and areas 16 times
    • 96 cm², multiplying the area by 4 for the larger scale number
12. 8.

    The lake covers 24 cm² on Map P. About how large is it on the ground, Noah asks?

    • About 6 km²: each cm² stands for 0.25 km²
    • About 1.5 km², since Map Q’s paper area stands for the ground area
    • About 12 km², multiplying 24 by the 0.5 km a centimeter stands for
    • About 60 km², converting 24 × 2,500,000,000 cm² into 10 times too many

13. 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.

14. 9.

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

    • Change it: 4.0°, since minutes are too small to count
    • Change it: 5.4°, because 54′ is written after the 4
    • Leave it: 54′ is written as 0.54 of a degree
    • Change it: 4°54′ is 4.9°, because 54′ is 54 ÷ 60 = 0.9°
15. 10.

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

    • Change it: Quito is south of the equator, so add: 38°34′
    • 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: 38°8′, since 21′ − 13′ = 8′ and the degrees stay