Question

Question # 24
Revisit
From a point, Ram walks 4km southwards and then 3km toward west to reach a point P. From
P, he walks 5km toward south and finally stops after walking 12km toward west. Find the
shortest distance between the destination and the starting point?
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Answer 1

Given:

First Ram walk 4 km southwards

Then 3 km towards west to reach a point P

Then from P, he walks 5 km towards south and finally walks 12 km towards west.

To find:

The shortest distance between the destination and the starting point.

Solution:

When Ram walks 4 km southwards, on the coordinate axis he reaches (0,-4).

Then when he walks 3 km west, his position will be (-3,-4).

After walking 5 km towards south, his position will be (-3,-9).

After walking 12 km towards west, the final position will be (-15,-9)

The shortest distance from the origin to the final will be =  (15² + 9²)^1/2

= (225 + 81)^1/2

= 306^1/2 = 17.5 km

Therefore, the shortest distance would be 17.5 km.

Answer 2

SOLUTION

GIVEN

• From a point, Ram walks 4km southwards

• Then 3km toward west to reach a point P

• From P, he walks 5km toward south

• Finally stops after walking 12km toward west.

TO DETERMINE

The shortest distance between the destination and the starting point

EVALUATION

Let S be the starting point from where Ram starts walking and F be the destination point

Now Ram walks 4 km southwards and moves to the point A

So the coordinates of A is ( 0, - 4 )

Now Ram walks 3 km toward west to reach a point P

So the coordinates of the point P is ( - 3, - 4 )

Again From P , Ram walks 5 km toward South

Suppose Ram arrives at B

So the coordinates of the point B is ( - 3, - 9 )

Finally stops after walking 12km toward west.

So Ram arrives at F

Therefore the coordinates of the point F is

( - 15 , - 9 )

So we have to find the distance between S and F

The required distance

$= \sf{ \sqrt{ {( - 15 - 0)}^{2} + {( - 9 - 0)}^{2} } }$

$= \sf{ \sqrt{225 + 81} }$

$= \sf{ \sqrt{306} }$

$\sf{ = 17.49 \: \: (approx)}$

FINAL ANSWER

Hence the required distance = 17. 49 km

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