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Home » To conduct Sports Day activities, in your rectangular shaped school ground ABCD, lines have been drawn with chalk powder at a distance of 1 m each. 100 flower pots have been placed at a distance of 1 m from each other along AD, as shown in the following figure. Niharika runs 1/4 th the distance AD on the 2nd line and posts a green flag. Preet runs 1/5th 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?
To conduct Sports Day activities, in your rectangular shaped school ground ABCD, lines have been drawn with chalk powder at a distance of 1 m each. 100 flower pots have been placed at a distance of 1 m from each other along AD, as shown in the following figure. Niharika runs 1/4 th the distance AD on the 2nd line and posts a green flag. Preet runs 1/5th 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?
CBSE | Class 10 | Coordinate Geometry | Maths | NCERT
To conduct Sports Day activities, in your rectangular shaped school ground ABCD, lines have been drawn with chalk powder at a distance of 1 m each. 100 flower pots have been placed at a distance of 1 m from each other along AD, as shown in the following figure. Niharika runs 1/4 th the distance AD on the 2nd line and posts a green flag. Preet runs 1/5th 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?

We concluded from the given instructions that Niharika placed the green flag at 1/4th of the distance AD, or (1/4 ×100) m = 25 metres from the 2nd line’s starting point. As a result, this point’s coordinates are (2, 25).

Preet, too, placed a red flag at 1/5 of the distance AD, i.e., (1/5 100) m = 20m from the 8th line’s starting point. As a result, this point’s coordinates are (8, 20).

Using the distance formula, you can compute the distance between these flags.

The distance between two flags=\sqrt{{{\left( 8-2 \right)}^{2}}+{{\left( 20-25 \right)}^{2}}}=\sqrt{36+25}=\sqrt{61}m

The mid-point of the line connecting these sites is where Rashmi should place her blue flag. Let’s call this point P. (x, y).

x = (2 + 8)/2 = 10/2 = 5 and y = (20 + 25)/2 = 45/2

Therefore, P( x, y) = (5, 45/2) As a result, Rashmi should place her blue flag on the 5th line at 45/2 = 22.5m.

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