If Joy has to post a flag at one-fifth distance from green flag in the line segment joining the green and red flags, then where should he post his flag?

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Solution

Q.
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 the given figure below.

Niharika runs 1/4 of the distance AD on the 2nd line and posts a green flag. Preet runs 1/5 of the distance ADon the eighth line and posts a red flag.

Based on the above information answer the following questions:

(iii) (b) If Joy has to post a flag at one-fifth distance from green flag in the line segment joining the green and red flags, then where should he post his flag

1 $F = (\frac{16}{5}, 24)$

2 $F = (\frac{16}{5}, 21)$

3 $F = (\frac{- 16}{5}, 24)$

4 $F = (\frac{16}{2}, 24)$

Ans.
(1)

Let the coordinates of the flag F, posted by Joy, be F(x,y).

Using section formula (internal),
Joy posts the flag at one-fifth of the distance from the green flag towards the red flag:

$x = \frac{1 \cdot 8 + 4 \cdot 2}{1 + 4} = \frac{8 + 8}{5} = \frac{16}{5} y = \frac{1 \cdot 20 + 4 \cdot 25}{1 + 4} = \frac{20 + 100}{5} = \frac{120}{5} = 24 T h u s, F = (\frac{16}{5}, 24)$

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