35. If Joy has to post a flag at one-fourth distance from green flag, in the line segment joining the green and red flags, then where should he post his flag?
Answers
Answer:
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Given : The tracks are being marked with a gap of 1m each in the form of straight lines.
100 flower pots are placed with a distance of 1m each along AD
Dhriti runs one fourth of the distance in the second line along AD and posts a green flag
Reshma runs one fifth of the distance AD in the eighth line and posts a red flag.
To Find : Joy has to post a flag at one-fourth distance from green flag in the line segment joining the green and red flags, then where should he post his flag?
Solution:
Dhriti runs one fourth of the distance in the second line along AD and posts a green flag.
2nd row hence x coordinate = 2
one fourth of the distance = 100/4 = 25 m
=> Green flag = (2 , 25)
Reshma runs one fifth of the distance AD in the eighth line and posts a red flag.
8th row hence x coordinate = 8
one fifth of the distance = 100/5 = 20 m
=> Red flag = (8 , 20)
Joy has to post a flag at one-fourth distance from green flag (2, 25) in the line segment joining the green (2 , 25) and red flags ( 8 , 20)
one-fourth distance from green flag means three-fourth distance from red flag
Hence flag divided green (2 , 25) and red flags ( 8 , 20) in 1 : 3 ratio
Coordinates of Flag posted by Joy = ( 1* 8 + 3 * 2)/4 , (1 * 20 + 3 * 25)/4
= ( 14/4 , 95/4)
= (3.5 , 23.75)
Coordinates of Flag posted by Joy = (3.5 , 23.75)
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