To conduct Sports Day activities, in your rectangular shaped school ground $ABCD$, lines have been drawn with chalk powder at a distance of 1 m each. 100 flower pots have been placed at a distance of 1 m from each other along AD, as shown in given figure below. Niharika runs $\frac{1}{4}$th the distance $AD$ on the 2nd line and posts a green flag. Preet runs $\frac{1}{5}$th distance $AD$ on the eighth line and posts a red flag. What is the distance between both the flags? If Rashmi has to post a blue flag exactly halfway between the line segment joining the two flags, where should she post her flag?
Given:
To conduct Sports Day activities, in your rectangular shaped school ground $ABCD$, lines have been drawn with chalk powder at a distance of 1 m each.
100 flower pots have been placed at a distance of 1 m from each other along AD. Niharika runs $\frac{1}{4}$th the distance $AD$ on the 2nd line and posts a green flag. Preet runs $\frac{1}{5}$th distance $AD$ on the eighth line and posts a red flag.
To do:
We have to find the distance between both the flags and if Rashmi has to post a blue flag exactly halfway between the line segment joining the two flags, the distance at which she should post her flag.
Solution:
y-coordinate of the green flag $=\frac{1}{4}\times100$
$= 25$
This implies,
Coordinates of the green flag are $P (2, 25)$
y-coordinate of the red flag $= \frac{1}{5}\times100$
$= 20$
This implies,
Coordinates of red flag are $Q (8, 20)$
Using the division formula
$(x,y)=[\frac{m x_{2}+n x_{1}}{m+n}, \frac{m y_{2}+n y_{1}}{m+n}]$
The distance between two points is
$\mathrm{PQ}=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$
$\mathrm{PQ}=\sqrt{(8-2)^{2}+(20-25)^{2}}$
$=\sqrt{36+25}$
$=\sqrt{61} \mathrm{~m}$
Position of the blue flag $=$ The mid-point of $\mathrm{PQ}$
$=\frac{2+8}{2}, \frac{25+20}{2}$
$=(5, 22.5)$
The blue flag is in the 5th line at a distance of $22.5\ m$.
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