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 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

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?

   • The gap should be 30.26° rather than 30°26′, with a 111 km degree
   • 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
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 93 km at Phoenix
   • 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 3,400 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
   • About 3,900 km: 4.9° + 30.43° of both gaps at 111 km a degree
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 3,300 km, the sum of the two legs, 544 + 2,740
   • About 2,800 km, the diagonal, a little more than the 2,740 km leg
   • About 2,200 km, the longer leg minus the shorter
   • Under 2,740 km, since a diagonal cuts the corner and is shorter than the longer leg

8. 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.

9. 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
   • 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
10. 7.

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

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

11. 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.

12. 8.

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

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

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°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
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