7.3 Map Reading and Grid Navigation
Key Takeaways
- Right turns rotate your facing direction clockwise (N to E to S to W to N) and left turns rotate it counterclockwise, and this holds regardless of which direction you started facing
- Track your facing direction explicitly after every turn in a multi-step route - writing N/E/S/W after each step, or sketching a quick arrow, prevents the single most common error on turn-sequence items
- Net displacement after a multi-leg route is found by summing north/south movement separately from east/west movement, letting opposite directions on the same axis cancel out - not by adding every leg's distance together
- On a simple street grid, the block-distance between two intersections equals the number of streets between them plus the number of avenues between them, not a shorter diagonal or straight-line distance
- A route with fewer turns is not automatically the shortest one - always compare total block count between candidate routes, since an extra turn can still produce a shorter overall path
Map Reading and Grid Navigation
Quick Answer: Section B map items test three related skills: tracking which way you are facing after a sequence of turns, calculating your net position after a route with several legs in different directions, and reading distances on a simple street grid. All three reward slowing down enough to track information explicitly - on paper or in a clear mental step-by-step - rather than trying to picture the whole route at once.
Compass Directions and the Turn-Tracking Rule
Every map item assumes the same eight-direction compass, and a fixed rule governs what a 90-degree turn does to your facing direction: a right turn moves you one step clockwise through North, East, South, West, and back to North; a left turn moves you one step counterclockwise through the same four directions in reverse.
| Current facing | After one right turn | After one left turn |
|---|---|---|
| North | East | West |
| East | South | North |
| South | West | East |
| West | North | South |
This single table resolves any single-turn question instantly, but Section B items typically stack two, three, or even four turns in a row, and the most common error on these items is losing track of the facing direction partway through the sequence - defaulting back to the original starting direction, or assuming two turns in the same direction cancel out when they actually compound. Two right turns from any starting direction do not return you to that starting direction; they rotate you a full 180 degrees to face the opposite way. From North, two right turns land you facing South, not North. The only way to reliably avoid this error under time pressure is to update your facing after each individual turn, one step at a time, rather than trying to calculate the combined effect of several turns in a single mental leap.
A Worked Turn-Sequence Example
Consider an original scenario: an officer begins a foot patrol facing north, turns right at the first corner, walks half a block, turns right again at the next corner, and then turns left at a final corner. Which direction is the officer now facing?
Working through it one turn at a time: starting facing North, the first right turn puts the officer facing East. The second right turn, applied to that new East heading, puts the officer facing South. The final turn is a left turn applied to that South heading, which puts the officer facing East. The officer ends the sequence facing East - not North, and not South, both of which are tempting shortcuts if the turns are combined in one step instead of tracked individually. Saying the headings to yourself one at a time - N, then E, then S, then E - as each turn is applied takes only a few seconds and removes essentially all risk of this kind of error, which matters because you should not count on having scratch paper to write them down.
Common Turn-Tracking Traps
| Trap | What goes wrong | How to avoid it |
|---|---|---|
| Assuming two turns in the same direction cancel out | They compound instead - two rights from North give South, not North | Update facing after every single turn, never combine turns mentally |
| Losing track of which turn is "first" in a written sequence | Applying the turns in reverse order changes the final facing entirely | Read the sequence in the order given, left to right, top to bottom |
| Confusing a turn direction with a compass direction | "Turn right" is relative to current facing, not a fixed compass direction | A right turn always means clockwise from wherever you currently face |
| Forgetting a turn buried in a longer sentence | A four-turn sequence described in one long sentence hides a step | Count the number of turn phrases ("turn right," "turn left") before starting to track them |
Net Displacement Across a Multi-Leg Route
A second common item type describes a route made of several straight-line legs in different directions and asks for the officer's net position relative to the starting point - not the total distance walked, but the straight-line displacement once opposite directions on the same axis have canceled out.
The reliable method is to separate every leg into its north-south component and its east-west component, add up each axis separately, and only then combine the two totals into a final answer.
Consider an original scenario: an officer's patrol route covers, in order, 5 blocks north, 2 blocks west, 3 blocks south, and 4 blocks east. What is the officer's net position relative to the starting point?
| Leg | Direction | North-South effect | East-West effect |
|---|---|---|---|
| 1 | 5 blocks north | +5 north | 0 |
| 2 | 2 blocks west | 0 | -2 east (i.e., 2 west) |
| 3 | 3 blocks south | -3 north (i.e., 3 south) | 0 |
| 4 | 4 blocks east | 0 | +4 east |
| Totals | 5 - 3 = 2 north | -2 + 4 = 2 east |
Adding the north-south column gives a net of 2 blocks north (5 blocks north minus 3 blocks south). Adding the east-west column gives a net of 2 blocks east (4 blocks east minus 2 blocks west). The officer's net displacement from the starting point is therefore 2 blocks north and 2 blocks east - even though the total distance actually walked along the route was 5 + 2 + 3 + 4 = 14 blocks. A common wrong answer on this style of question simply adds every leg together and reports 14 blocks in some single direction, which conflates total distance traveled with net displacement - two genuinely different quantities that a map item is specifically designed to test the difference between.
Once net displacement is known, the shortest path back to the starting point is simply the reverse of that net displacement, not a reversal of the entire original route: from 2 blocks north and 2 blocks east of the start, the shortest way back is 2 blocks south and 2 blocks west, a 4-block trip, regardless of how many blocks the original winding route actually covered.
Reading Distance on a Simple Street Grid
A related but distinct skill involves a described grid of numbered streets running one direction and lettered avenues running the perpendicular direction, with locations given as street-and-avenue intersections. On this kind of grid, the block-distance between any two intersections is found by adding the number of streets between them to the number of avenues between them - never by estimating a shorter diagonal distance, since movement is restricted to the grid lines themselves.
Consider an original scenario: on a town grid where numbered streets run east-west and lettered avenues run north-south, a patrol unit is at the intersection of 2nd Street and Avenue C and receives a call at the intersection of 5th Street and Avenue F. The street difference is 5 minus 2, or 3 streets; the avenue difference is F minus C, or 3 avenues. The total grid distance is 3 plus 3, or 6 blocks - not a shorter number arrived at by imagining a straight diagonal line across the grid, which is not a path the unit can actually drive or walk.
Comparing Two Candidate Routes
When a Section B item offers two different described routes to the same destination, the number of turns each route requires is not the deciding factor - total block count is. A route with three turns that covers 6 blocks is shorter than a route with only one turn that covers 9 blocks, even though the second route looks simpler on paper. The correct process is to add up the blocks in each candidate route separately, compare the two totals directly, and select the smaller one; only if both routes cover an identical number of blocks does a secondary factor, such as fewer turns or a route matching the initial facing direction without doubling back, become the appropriate tiebreaker.
An officer begins facing east and executes two consecutive left turns. Which direction is the officer now facing?
A patrol route covers, in order, 6 blocks north, 4 blocks east, 2 blocks south, and 4 blocks west. What is the officer's net displacement from the starting point?
On a town grid where numbered streets run east-west and lettered avenues run north-south, a unit at the intersection of 3rd Street and Avenue B is dispatched to the intersection of 7th Street and Avenue E. What is the grid distance between these two intersections?
Two candidate routes are offered to the same destination: Route A requires one turn and covers 9 total blocks, while Route B requires three turns and covers 7 total blocks. Which route is actually shorter, and why?