Question

In order to conduct Sports Day activities in your School, lines have been drawn with chalk powder at a distance of 1 m each, in a rectangular shaped ground ABCD, 100 flowerpots have been placed at a distance of 1 m from each other along AD, as shown in given figure below. Niharika runs 1/4 th the distance AD on the 2nd line and posts a green flag. Preet runs 1/5 th distance AD on the eighth line and posts a red flag

1. Find the position of green flag

a) (2,25)

b) (2,0.25)

c) (25,2)

d) (0, -25)

2. Find the position of red flag

a) (8,0)

b) (20,8)

c) (8,20)

d) (8,0.2)

3. What is the distance between both the flags? 

a).√41

b) √11

c) √61

d) √51

4. If Rashmi has to post a blue flag exactly halfway between the line segment joining the two flags, where should she post her flag?

a) (5, 22.5)

b) (10,22)

c) (2,8.5)

d) (2.5,20)

5. 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?

a) (3.5,24)

b) (0.5,12.5)

c) (2.25,8.5)

d) (25,20)

Answer 1

1. a) (2,25)

Position of green flag = Point G

= (2,25)

2. c) (8,20)

Position of green flag = Point R

= (8,20)

3. c) √61

Distance between both flages = RG

4. a) (5, 22.5)

Since Rashmi had to post a blue flag exactly halfway between the line segment joining the two flags

It will be the mid-point of RG

Thus, our diagram looks like

Substituting the value in the formula

∴ Rashmi (x,y) = (5,22.5)

5. a) (3.5,24)

Now, Joy had to post a flag at one-fourth distance from green flag, in the line segment joining the green and red flags

Thus,

Distance between Green Flag & joy

= 1/4 x Distance between Green and Red Flag

GJ = 1/4 x GR

Thus, joy divides GR in the ratio 1: 3

Thus,

Required Point = (3.5, 23.75)

Answer 2

1. a) (2,25)

2. c) (8,20)

3. c) √61

4. a) (5, 22.5)

5. a) (3.5,24)