To conduct Sports Day activities, in your rectangular shaped school ground ABCD, lines have been drawn with chalk powder at a distance of 1m each. 100 flower pots have been placed at a distance of 1m from each other along AD, as shown in Fig. 7.12. Niharika runs $\frac{1}{4}$ th the distance AD on the 2nd line and posts a green flag. Preet runs $\frac{1}{5}$ th the distance AD on the eighth line and posts a red flag. What is the distance between both the flags? If Rashmi has to post a blue flag exactly halfway between the line segment joining the two flags, where should she post her flag?

 

 

 

 

 

 

 

 

 

 

 

 

Given: 100 flower pots have been placed at a distance of 1m from each other along AD.

Let Niharika post the green flag at a distance P, that is, (1/4 × 100) m = 25 m from the starting point of the 2^nd line. Therefore, the coordinates of the point P are (2, 25).

Similarly, Preet posted a red flag at the distance Q, that is, (1/5 × 100) m = 20 m from the starting point of the 8^th line. Therefore, the coordinates of the point Q are (8, 20).

To find the distance between these flags, we will find PQ using the distance formula,

PQ = √ (x₂ - x₁ )² + (y₂ - y₁)²

PQ = √ (8 - 2)² + (20 - 25)²

= √36 + 25

= √61 m

Let the point be A (x, y) at which Rashmi should post her blue flag exactly at the centre of the line joining the coordinates P(2, 25) and Q(8, 20)

By midpoint formula,

P (x, y) = [(x₂ + x₁) / 2 , (y₂ + y₁) / 2]

P(x, y) = [(2 + 8) / 2, (25 + 20) / 2]

P(x, y) = (10/2, 45/2)

P(x, y) = (5, 22.5)

Therefore, Rashmi should post her blue flag at a distance of 22.5 m on the 5^th line.