 Hello friends, welcome to the session. I am Malka. Let's discuss the given question to conduct spots day activities in your rectangular shaped school ground ABCD lines have been drawn with chalk powder at a distance of one meter each 100 flower pots have been placed at a distance of one meter from each other Along AD as shown in the figure 7.12 Nehari ka runs one fourth the distance AD on the second line and post a Green flag breath runs one fifth the distance AD on the eighth line and post a red flag What is the distance between? both the Flags if the Rashmi has to post a blue flag Exactly halfway between the line segment joining the two flags. Where should she post her flag? Now here is the given figure according to the question where a BCD is a rectangular School ground and the girl with a green flag is Nehari ka Which has covered the one fourth of the distance AD on the second line and girl with the red flag is Free who has covered one fifth the distance AD on the eighth line Now we have to find the distance between both these flags Now before starting with the solution, I would like to tell you the basic idea behind the question It is the distance Formula as we all know For a given line segment with coordinate with points a and b and the coordinates of AR x1 y1 and Coordinates of VR x2 y2 so this is between a and b is given by square root of x1 minus x2 whole square plus y1 minus y2 Whole square. So this is the distance between a and b Now let's start with the solution Now first of all we find the coordinates of the point that is position of Nehari ka and Preet in rectangular shape ground. So position of Nehari ka is She was on the second line so it is second and Since she has covered One-fourth the distance AD and we know that the distance AD is hundred meter. So One-fourth of hundred is 25 So the position of Nehari ka is the coordinates to and 25 similarly we write the position of Preet So it is She goes on the eighth line. So x coordinate is 8 and she has covered one-fifth the distance AD So it will be 20 Now we have to find the distance between the both the flags of Nehari ka and Preet So we'll use the distance formula therefore distance between flags is Square root of x1 minus x2 that is 2 minus 8 whole square plus y1 minus y2 that is 25 minus 20 whole square So this is equal to square root of We get 6 so 36 6 whole square is 36 plus 5 5 square is 25 so this is equal to square root of 61 Meter therefore the distance between flags is square root of 61 meters now again, we have to show that if Rashmi Has to plot a blue flag exactly half way Between the line segment joining the two flags then we have to find where should she post her flag Now since we have to find the half way that is the midpoint So we'll use the midpoint formula to find her position that is The fact to find the position of Rashmi where she'll post the blue flag. So we say that Rashmi has to post post a blue flag exactly half way then Using midpoint formula we find the position of Blue flag Which is 2 plus 8 upon 2 and 25 plus 20 upon 2 that is x1 plus x2 upon 2 and y1 plus y2 upon 2 which is equal to 5 and 45 upon 2 so From the figure we see that it will be the fifth line at a distance of 22.5 meters. So this is fifth line distance of 22.5 meters now therefore square root of 61 meter is the distance between flags and the fifth line distance of 22.5 meter is the position of blue flag So the distance between the green flag and the red flag will be square root of 61 meters and the position of the blue flag will be the fifth line and 22.5 meters along the line AD. Hope you understood both the parts and enjoyed the session. Goodbye and take care