Question

Find the corner of wheat growing field. Rajesh moves 3 steps towards north and 4 steps towards east and reaches diagonally heading corner of plot.From the same point , Harish moves 4 steps towards east and 3 steps towards north and reaches the same point .Taking east –west direction as x-axis and north-south direction as y-axis and starting point as origin ,write the coordinates of points at which two persons meet .A third person Karim moves straight way towards the point where the two persons meet together .Has the third person travelled less distance ?Can you find distance travelled by third person ?Is the action of third person is correct ?Write value depicted by the question​

Answer 1

We are given that

Rajesh moves 3 steps north and then 4 steps towards east from a point.

Harish moves 4 steps east and then 3 steps towards north from the same point.

Rajesh and Harish then reach to same point.

Please refer to the attached image for clarification of the question.

East West direction is taken as x axis and

North South direction is taken as y axis.

Let, Rajesh and Harish were at point O(0,0) in the beginning.

Rajesh moves 3 steps north i.e. on positive y axis and moves to point P(0,3).

then 4 steps towards east.

i.e. reaches to point A(4,3).

Rajesh moves 3 steps north i.e. on positive y axis and moves to point P(0,3).

then 4 steps towards east.

i.e. reaches to point A(4,3).

Total distance traveled by Rajesh = 3+4 = 7 steps

Harish moves 4 steps towards east i.e. reaches to point Q(4,0) on x axis.

then 3 steps towards east.

i.e. reaches to point A(4,3).

Total distance traveled by Harish = 4+3 = 7 steps

The corners of field are O(0,0), P(0,3), Q(4,0) and A(4,3).

Third person Karim travels in a straight line towards point A(4,3)

So, distance traveled by the 3rd person = side OA.

Distance formula

:

$D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Here,

$x_2 = 4\\x_1 = 0\\y_2 = 3\\y_1 = 0$

$OA = \sqrt{(4-0)^2+(3-0)^2}\\\Rightarrow OA = \sqrt{(4)^2+(3^2)}\\\Rightarrow OA = \sqrt{16+9}\\\Rightarrow OA = \sqrt{25} = 5\ steps$

So, 3rd person Karim has traveled a lesser distance , only 5 steps taken to reach the same point.