NCERT Solutions
Class 10 Maths
Coordinate Geometry

Ex. 7.2 Q.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?

It can be observed that Niharika posted the green flag at of the distance AD i.e., (1/4 * 100)
= 25 m from the starting point of 2nd line. Therefore, the coordinates of this point G is (2, 25).
Similarly, Preet posted red flag at of the distance AD i.e., m from the (1/5 * 100) = 25 m from
the starting point of 8th line. Therefore, the coordinates of this point R are (8, 20).
Distance between these flags by using distance formula = GR
= √{(8 - 20)2 + (25 - 20)2} = √ (36 + 25) = √61 m
The point at which Rashmi should post her blue flag is the mid-point of the line joining these
points. Let this point be A (x, y).
Now, x = (2 + 8)/2 = 12/2 = 5
and y = (25 + 20)/2 = 45/2 = 22.5
Hence, A(x, y) = (5, 22.5)
Therefore, Rashmi should post her blue flag at 22.5m on 5th line.