Direction and distance questions test whether you can track movement on a simple map and identify a final direction or shortest distance. Draw every movement as an arrow rather than trying to calculate the route only in your head.

Basic directions

• North is up, south is down, east is right, and west is left.
• North-east, north-west, south-east, and south-west are diagonal directions.
• Opposite pairs are north-south, east-west, north-east-south-west, and north-west-south-east.

Tracking movement

Choose a starting point, mark it as the origin, and draw each move in sequence. Combine movements along the same axis: east and west offset each other, as do north and south. The remaining horizontal and vertical movement show the final position.

Finding the final direction

Compare the final position with the starting point. A position to the right and above the start is north-east; right and below is south-east; left and above is north-west; left and below is south-west.

Shortest distance

When the final horizontal and vertical distances form a right triangle, use the Pythagorean theorem. If the horizontal distance is $a$ and the vertical distance is b, the shortest distance is square root of (a squared + b squared).

• $3, 4, 5$ is the most common right-triangle set.
• $5, 12, 13$ and $8, 15, 17$ are also useful sets.
• For straight-line movement on one axis, add or subtract distances directly.

Turning directions

• A right turn from north faces east; a left turn from north faces west.
• A right turn from east faces south; a left turn from east faces north.
• A 180-degree turn changes a direction to its opposite.
• Always take turns from the traveler's current facing direction.

A reliable solving method

1. Draw a compass with north at the top.
2. Mark the start point and trace every stated movement.
3. Track turns before drawing the next movement.
4. Cancel opposite movements to find the final position.
5. Use the Pythagorean theorem only for the straight-line shortest distance.

Common mistakes

• Adding total path length when the question asks for shortest distance.
• Reversing east and west or north and south on the diagram.
• Taking a turn from the original direction rather than the current one.
• Forgetting to cancel movements in opposite directions.

Quick revision summary

• Draw each move and mark the compass directions.
• Find final direction by comparing final and starting positions.
• Use square root of (a squared + b squared) for diagonal shortest distance.
• Read every turn from the current direction of travel.