Ex 7.2, 3
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 1/4th 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?
Here let us draw a simpler figure of
what is given
Here , given that there are 100 flowers
between A & D at 1m distance each
Niharika runs 1/4th of the distance
AD on 2nd line
So, Niharika x−ordinate = 2
Niharika y – ordinate = 1/4 × 100 = 25
So, Niharika (2, 25)
Similarly,
Preet runs 1/5th of the distance AD on 2nd line
So, Preet x−ordinate = 8
Preet y – ordinate = 1/5 × 100 = 20
So, Preet (8, 20)
We have to find distance between
Niharika and Preet’s flag
Using distance formula
NP = √((𝑥2 −𝑥1)2+(𝑦2 −𝑦1)2)
x1 = 2, y1 = 25
x2 = 8, y2 = 20
Putting values in formula
NP = √(( 8 −2)2+(20 −25)2)
= √((6)2+(−5)2)
= √((6)2+(5)2)
= √(36+25)
= √61
Hence,
The distance between both flags = √𝟔𝟏 metres
Also, it is given that Rashmi had to post a blue flag exactly halfway between the line segment joining the two flags
So,
Here, x = (𝑥1 + 𝑥2)/2
y = (𝑦1 + 𝑦2)/2
Where
x1 = 2, y1 = 25
x2 = 8, y2 = 20
Substituting the value in the formula
x = 5, y = 22.5
Therefore,
Rashmi (x, y) = (5, 22.5)
Therefore Rashmi would post her flag in the 5th line at 22.5 metre
x = (𝑥1 + 𝑥2)/2
x = (2 + 8)/2
x = 10/2 x = 5
y = (𝑦1 + 𝑦2)/2
y = (25 + 20)/2
y = 45/2
y = 22.5

Made by

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.