City Cycle Connections

Use coordinates and absolute value to plan bike routes.

Read the City Map

Use the map and landmark key. Each grid unit represents 100 meters. East is right, and north is up.

A: Library • B: Transit station • C: Plaza • D: Bike repair shop • E: Café • F: Fountain • G: Bike racks

What are the coordinates of the transit station, B?

A. (4, 3)B. (−3, 4)C. (3, 4)D. (3, −4)

Which ordered pair locates the fountain, F?

A. (−2, −1)B. (−1, −2)C. (2, −1)D. (−2, 1)

The library and transit station have the same y-coordinate. Find the distance directly between them.

Distance: grid units

Find the distance directly from the transit station to the plaza.

Distance: grid units

The café and library are both west of the y-axis. How far apart are they?

Distance: grid units

Plan and Check Routes

Use the city map from Section 1. Routes follow horizontal or vertical lines. Each grid unit represents 100 meters.

Which expression gives the distance in grid units from the fountain, F, to the café, E?

A. |−2| + |−2|B. |4| − |−1|C. |−2 − (−2)|D. |4| + |−1|

A bike courier rides directly east from the repair shop, D, to the plaza, C. How many meters is this trip?

Trip length: meters

Nia rides from the library to the transit station, then south to the plaza. How far does she ride in all?

Total distance: meters

A cycling club plans a loop from A to B to C to D and back to A. Its distance limit is 3,500 meters. Which statement is correct?

A. The loop is 1,800 meters, so it is within the limit.B. The loop is 3,600 meters, so it exceeds the limit by 100 meters.C. The loop is 3,600 meters, so it exceeds the limit by 1,000 meters.D. The loop is 2,700 meters, so it is within the limit.

10.

Omar says the café, E, and transit station, B, are 1 grid unit apart because |3| − |−2| = 1. Explain his mistake and give the correct distance in grid units.

Map a New Bike Corridor

A separate planning map shows proposed stops. Each grid unit still represents 100 meters.

11.

Plot and label four proposed stops: H(−4, 6), J(5, 6), K(5, −2), and L(−4, −2). Connect H to J, J to K, K to L, and L to H.

12.

A route sign at H will show the distance directly east to J. What distance should the sign display?

Distance: meters

13.

Luis rides from J south to K, then west to L. How many grid units does he travel altogether?

Total distance: grid units

14.

A new water station, M, will be on the segment from K to L, exactly 600 meters west of K. Find its x-coordinate.

M = (, −2)