Direction and Distance
Direction and Distance is an important topic of the reasoning paper of ADRE Grade IV. In these questions a person or a vehicle moves in different directions for some distance, and the candidate has to work out either the final direction from the starting point or the shortest distance between the starting point and the ending point. The questions are based on very simple ideas, but they need neat diagrams. A candidate who draws a small, clear figure for every question can solve this topic with almost no mistakes and in very little time.
The Four Main Directions
The four main directions are North, South, East and West. North is taken as the upward direction and South as the downward direction on the page. East is to the right and West is to the left. Between the main directions lie the four sub-directions, namely North-East, North-West, South-East and South-West. A full turn of directions is 360 degrees, so each main direction is ninety degrees from the next and each sub-direction is forty-five degrees from the main directions beside it. Knowing these positions by heart is the first step of the topic.
Drawing the Direction Diagram
To solve a direction question, always draw the directions on rough paper. Mark the starting point and draw a small cross for the four main directions and the four sub-directions. Then move the pen according to the question, turning left or right as instructed. When a person turns left, the facing direction changes by ninety degrees anticlockwise, and when a person turns right, it changes by ninety degrees clockwise. Facing North and turning left means facing West, facing North and turning right means facing East. Keeping the diagram small and neat prevents almost all errors.
Finding the Shortest Distance
The shortest distance between the starting point and the ending point is found by using the Pythagorean theorem. If the movement forms a right-angled triangle with two sides of a and b, then the shortest distance is the square root of a squared plus b squared. For example, if a person walks three kilometres North and then four kilometres East, the shortest distance from the start is the square root of nine plus sixteen, which is the square root of twenty-five, that is five kilometres. Common triples such as three, four, five and six, eight, ten should be remembered.
Common Patterns in Questions
- Walking in two directions and asking the final direction.
- Walking in several directions and asking the shortest distance.
- Turning left or right a number of times and asking the final facing.
- Shadow-based questions, where the sun's position decides the direction.
- Clock-based direction, where the hour hand points to a direction.
Worked Example
Suppose a man walks five kilometres towards the North, then turns right and walks five kilometres, and then turns right again and walks five kilometres. Starting from the South facing North, after the first right turn he faces East, and after the second right turn he faces South. So he ends five kilometres to the East of the starting point. The shortest distance from the start is five kilometres, because his final position is directly East of the start. This example shows how each turn must be worked out step by step.
How This Topic Appears in the Examination
Direction and distance usually appears as two to four objective questions of one mark each. The questions describe the movement of a person or an object and ask either the final direction or the shortest distance. Some questions give the final position and ask for the starting direction. Most questions can be solved in a minute once the diagram is drawn. This topic is a reliable source of marks because the method is fixed and the figures are simple.
Memory Tips
Always use the rule of right and left turns: a right turn from any direction reaches the direction ninety degrees clockwise, and a left turn reaches the direction ninety degrees anticlockwise. Draw the cross of directions first and mark North as up, South as down, East as right and West as left. Remember the common Pythagorean triples by heart, such as three-four-five, six-eight-ten and five-twelve-thirteen. In shadow questions, remember that in the morning the shadow falls to the West and in the evening to the East.
Common Mistakes to Avoid
- Turning left instead of right, or the reverse.
- Forgetting the direction a person is already facing before turning.
- Adding distances straight instead of using the Pythagorean theorem.
- Drawing a large or untidy diagram and losing track of the path.
- Confusing the final direction with the shortest distance between two points.
How to Prepare This Topic
- Learn the eight directions and their positions by heart.
- Practise drawing the direction cross for every question.
- Memorise the common Pythagorean triples.
- Solve at least ten direction questions every day.
- Revise shadow and clock based direction rules separately.
Frequently Asked Questions
How many directions are there in all?
There are eight directions in all: the four main directions North, South, East and West, and the four sub-directions North-East, North-West, South-East and South-West.
How is the shortest distance calculated?
The shortest distance is calculated using the Pythagorean theorem. If the two sides are a and b, the distance is the square root of a squared plus b squared.
Facing North, which direction is to my right?
Facing North, the East is to the right and the West is to the left. A right turn takes you to the East and a left turn to the West.
What is the direction of a shadow in the morning?
In the morning the sun rises in the East, so the shadow falls towards the West. In the evening the sun sets in the West, so the shadow falls towards the East.
Should I always draw a diagram?
Yes. Drawing a small, neat diagram is the safest method and prevents almost all mistakes, even in questions with only one or two turns.