A City school is organizing Annual sports event in a rectangular shaped ground
ABCD. 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 as shown in the
following figure. 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.
(i) What are the coordinates of the Flag posted by
Reshma?
(a) (2, 25) (b) (8, 25)
(c) (2, 20) (d) (8, 20)
(ii) If Swathi has to post a blue flag exactly halfway
between the line segment joining the two flags,
the coordinates where she should post her flag?
(a) (5, 45) (b) (5, 50)
(c) (5, 22.5) (d) (5, 25.5)
(iii) What is the distance between Green flag and Red
flag?
(a) 51m (b) 61m
(c) 71m (d) 81m
(iv) Consider AB as x-axis and AD as y-axis, then what will be the distance of Red flag
from the y-axis?
(a) 5units (b) 22.5units (c) 8units (d) 2units
(v) The flag posted by Swathi divides the line segment by joining the Green flag and Red
flag in the ratio
(a) 1:2 (b) 1:1 (c) 2:1 (d) 1:3
Answers
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 : Coordinates of the Flag posted by Reshma
Swathi has to post a blue flag exactly halfway between the line segment joining the two flags, the coordinates where she should post her flag
distance between Green flag and Red flag
distance of Red flag from the y-axis?
The flag posted by Swathi divides the line segment by joining the Green flag and Red flag in the ratio
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.
8t row hence x coordinate = 8
one fifth of the distance = 100/5 = 20 m
=> Red flag = (8 , 20)
coordinates of the Flag posted by Reshma = Red flag = (8 , 20)
Swathi has to post a blue flag exactly halfway between the line segment joining the two flags, Green flag (2 , 25) and Red flag = (8 , 20)
= (2 + 8)/2 , (25 + 20)/2
=10/2 , 45/2
= 5 ,22.5
Swathi posted flag at ( 5 , 22.5)
distance between Green flag (2 , 25) and Red flag = (8 , 20)
= √(8 - 2)² +(20 - 25)²
= √36 + 25
= √61 m
Distance of Red flag (8 , 20) from the y-axis is 8 units
flag posted by Swathi divides the line segment by joining the Green flag and Red flag in the ratio 1: 1
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