Question

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 figure. 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?

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

FIGURE in the attachment

ATQ,

100 flower pots have been placed at a distance of 1 m from each other along AD.

i.e AD = 100m

➡ Distance travelled by niharika = 1/4 × 100

= 25m

» Her position :- (2, 25)

➡ Distance travelled by Preet = 1/5 × 100

= 20m

» His position :- (8, 20)

Now distance between Niharika and Preet :-

Using distance formula :- √[(x2 - x1)² + (y2 - y1)²]

= √[(8 - 2)² + (20 - 25)²]

= √[(6)² + (-5)²]

= √(36 + 25)

= √61

Hence, the distance between both the flags is √61 m

Now, let M be the position of the blue flag which is posted by Rashmi in the halfway of the two flags (between (2,25) and (8,20))

Since it's the middle point, we can write

➡ M = [(x1 + x2)/2 , (y1 + y2)/2]

➡ M = [(2 + 8)/2 , (25 + 20)/2]

➡ M = (10/2 , 45/2)

➡ M = (5, 22.5)

Hence, the blue flag is on the 5th line at a distance of 12.5m