NCERT Solutions
Class 10 - Mathematics - Chapter 7: COORDINATE GEOMETRY - Exercise 7.2

Question 3

Let us choose a coordinate system on the ground with \(A\) as the origin \((0, 0)\), AD along the x-axis and AB along the y-axis. The flower pots are kept 1 m apart on AD and the chalk lines are also 1 m apart, so the length of AD is 100 m.

Niharika runs \(\tfrac{1}{4}\) of AD on the 2nd line. So the distance she runs along AD is \(\tfrac{1}{4} \times 100 = 25\) m. The 2nd line is 2 m above AD. Therefore, the coordinates of the green flag are \((25, 2)\).

Preet runs \(\tfrac{1}{5}\) of AD on the 8th line. So the distance he runs along AD is \(\tfrac{1}{5} \times 100 = 20\) m. The 8th line is 8 m above AD. Therefore, the coordinates of the red flag are \((20, 8)\).

Now, the distance between the flags is found using the distance formula between \((25, 2)\) and \((20, 8)\):

\( d = \sqrt{(25 - 20)^2 + (2 - 8)^2} = \sqrt{5^2 + (-6)^2} = \sqrt{25 + 36} = \sqrt{61} \text{ m}. \)

To find the position where Rashmi should post the blue flag, we need the midpoint of the line segment joining the two flags. The midpoint of \((25, 2)\) and \((20, 8)\) is

\( \left( \frac{25 + 20}{2}, \frac{2 + 8}{2} \right) = \left( \frac{45}{2}, 5 \right) = (22.5, 5). \)

Thus, Rashmi should post the blue flag on the 5th line at a distance of 22.5 m from A along AD.