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# 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 1/4 th the distance AD on the 2nd line and posts a green flag. Preet runs 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?

**Solution:**

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)

We know that the distance between the two points is given by the Distance Formula,

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.

**☛ Check: **Class 10 Maths NCERT Solutions Chapter 7

**Video Solution:**

## 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 1/4 th the distance AD on the 2nd line and posts a green flag. Preet runs 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?

NCERT Class 10 Maths Solutions Chapter 7 Exercise 7.2 Question 3

**Summary:**

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 with AD, as shown in the above figure. Niharika runs 1 th the distance AD on the 2nd line 1/4 and posts a green flag. Preet runs 1/5 th the distance AD on the eighth line and posts a red flag. The distance between both the flags are √61 m. If Rashmi has to post a blue flag exactly halfway between the line segment joining the two flags, she should post her blue flag at 22.5 m on the 5^{th} line.

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