Let ABCD be any rectangular ground. AB is alongxxaxis and AD is alongyyaxis.

The length of AD is 100 m.

The distance ran by Niharika onyyaxis is,

Distance=14×AD=14×100=25mDistance=14×AD=14×100=25m

The distance ran by Preet onyyaxis is,

Distance=15×AD=15×100=20mDistance=15×AD=15×100=20m

The coordinates of the flag posted by Niharika isN(2,25)N(2,25).

The coordinates of the flag posted by Preet isP(8,20)P(8,20).

According to the distance formula, the distance between the two pointsP(2,25)P(2,25)andN(8,20)N(8,20)is,

PN=√(8−2)2+(20−25)2=√36+25=√61mPN=(8−2)2+(20−25)2=36+25=61m

Let the coordinate of pointRR, where Rashmi has to post the flag at the line segmentPNPNbe(x,y)(x,y).

Since pointRRis the midpoint of the line segmentPNPN.

PR:RN=1:1PR:RN=1:1

From the section formula, the coordinate of the pointP(x,y)P(x,y)which divides the line segment joining the pointsA(x1,y1)A(x1,y1)andB(x2,y2)B(x2,y2)internally in the ratiom1:m2m1:m2is,

(x,y)=(m1x2+m2x1m1+m2,m1y2+m2y1m1+m2)(x,y)=(m1x2+m2x1m1+m2,m1y2+m2y1m1+m2)

Now, substitute the valuesx1,x2,y1andy2x1,x2,y1 andy2in above formula, we get,

x=1×2+1×81+1=2+82=5x=1×2+1×81+1=2+82=5

y=1×25+1×201+1=452=22.5y=1×25+1×201+1=452=22.5

The coordinate of pointPPis(5,22.5)(5,22.5)

Thus, Rashmi should post her flag in the fifth row at a distance of 22.5 m.