Distance

We will be asked to find out either of these two:

• the total distance covered by a particular person or object.
• minimum distance between initial and final point.

To find the minimum distance between the starting and end point, we use the Pythagoras Theorem.

Pythagoras Theorem

It is a relation among the three sides of a right angled triangle. It states that the square of the hypotenuse (the side opposite to the right angle) is equal to the sum of the squares of the other two sides. RQ (or QR) is the minimum or shortest distance to reach Q from R (or to reach R from Q).

Let’s see some examples and question types.

Type 1: Finding the Minimum Distance

In this type of questions, we are supposed to find out the minimum distance between the initial and the final points.

To do this, we use the Pythagoras Theorem.

Q. At the start of his journey, Punit walks for 3 km in the north direction. Thereafter, he turns right and walks 5 km, before again turning right and walking 9 km. Finally, he takes a left turn and walks 3 km. How far he must be from the starting point?

(a) 5 km   (b) 10 km   (c) 12 km   (d) 15 km

Explanation:

Let the starting point be P and end point be Q.
Path taken by Punit has been represented in the following figure: In triangle PQR, PQ can be calculated using the Pythagoras Theorem:
PQ² = 6² + 8²
or PQ = √(6² + 8²) = 10 km

Answer: (b)

Type 2: Finding the Total Distance

In this type of questions, we are supposed to find out the total distance covered by a particular person or object.

Q. Mohan walks 8 km towards east. Then, he turns right and walks 1 km, before taking a right turn again and walking 5 km. After this he takes a left turn and walks 3 km. How much distance has he travelled from the onset of his journey?

(a) 5 km   (b) 20 km   (c) 17 km   (d) 15 km

Explanation:

Following figure depicts the path travelled by Mohan: Therefore, total distance = 8 + 1 + 5 + 3 = 17 km

We could have solved the above question even without making the diagram, as we were just supposed to add the distances covered. Drawing diagram is more helpful if the shortest distance between the initial and end points has to be found out.

Answer: (c)