1. a) (2,25)
![](https://www.sarthaks.com/?qa=blob&qa_blobid=14641656333819229924)
Position of green flag = Point G
= (2,25)
2. c) (8,20)
![](https://www.sarthaks.com/?qa=blob&qa_blobid=14641656333819229924)
Position of green flag = Point R
= (8,20)
3. c) √61
![](https://www.sarthaks.com/?qa=blob&qa_blobid=14641656333819229924)
Distance between both flages = RG
![](https://www.sarthaks.com/?qa=blob&qa_blobid=6236280411176791326)
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
![](https://www.sarthaks.com/?qa=blob&qa_blobid=2710253322651041047)
Substituting the value in the formula
![](https://www.sarthaks.com/?qa=blob&qa_blobid=10062955835465146412)
∴ 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
![](https://www.sarthaks.com/?qa=blob&qa_blobid=3240616762721636502)
Thus,
Distance between Green Flag & joy
= 1/4 x Distance between Green and Red Flag
GJ = 1/4 x GR
![](https://www.sarthaks.com/?qa=blob&qa_blobid=14739743611763867258)
Thus, joy divides GR in the ratio 1: 3
![](https://www.sarthaks.com/?qa=blob&qa_blobid=4796451146793227858)
![](https://www.sarthaks.com/?qa=blob&qa_blobid=12616983535412487837)
Thus,
Required Point = (3.5, 23.75)