Question

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 Fig. Niharika runs $\frac{1}{4}$th the distance $AD$ on the $2$nd line and posts a green flag. Preet runs $\frac{1}{5}$th the 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?

Answer 1

$AD=100$ m and $AB=10$m

The coordinates of Niharika's flag $=(2,25)$ and the coordinates of Preet's flag $=(8,20)$.

$A(2,25)$ and $B(8,20)$

AB = $\sqrt{{(20-25)}^2+{(8-2)}^2}=\sqrt{(-5{)}^2+6^2}=\sqrt{25+36}=\sqrt{61}$

Distance between both flags is $\sqrt{61}$ m.

Rashmi has to place her flag at the midpoint of $AB$.

MIdpoint of AB = $(\frac{2+8}{2},\frac{25+20}{2})$ = $(5,22.5)$

Rashmi must place her flag along the fifth line at $22.5$ m from $A$.