Question

Question 3 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 the following figure. Niharika runs the distance AD on the 2 nd line and posts a green flag. Preet runs 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?

Class 10 - Math - Coordinate Geometry Page 167

Answer 1

Distance Formula

The distance between two points A(x1, y1) and B(x2, y2) is
 
AB =  √( x 2 - x1 ) ² + ( y 2 - y 1 ) ² 
 
.AB =  √( x 1 - x2 ) ² + ( y 1- y 2) ² 

AB =  √( difference of abscissae ) ² + ( difference of ordinates ) ² 


Midpoint:

The midpoint of a line segment divides it into two equal parts or in the ratio 1:1.
The midpoint of line segment joining the points (x1, y1) and (x2, y2) is   [(x1 +  x 2) /2 ,  (y 1 +  y2) /2 ]

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Solution:

From the Given figure , the position of green flag posted by Niharika is M & red flag posted by Preet is N


It can be observed that Niharika posted the green flag at 1/4th of the distance AD i.e., (1×100/4)m = 25m from the starting point of 2nd line.

Therefore, the coordinates of this point M is (2, 25).

Similarly, Preet posted red flag at 1/5 of the distance AD i.e., (1×100/5) m = 20m from the starting point of 8th line.

Therefore, the coordinates of this point N are (8, 20).

Distance between these flags by using distance formula = MN

Here x1= 2 ,y1= 25, x2= 8, y2= 20

MN =   √( x 2 - x1 ) ² + ( y 2 - y 1 ) ² 

MN = √ (8-2) ² + (20-25)² = √(6)² + (-5)² = √36 + 25 = √61

Hence , the distance between flags is √61 m

Let P be the position of the blue flag posted by Rashmi in the half way of line segment MN.

Then , coordinates  of P= [(x1 +  x 2) /2 ,  (y 1 +  y2) /2 ]

= ((2+8)/2) , (25+20)/2) = (10/2 , 45/2) = (5, 22.5)

Hence the blue flag is on the 5th line at a distance of 22.5 m above it..

Answer 2

Answer:

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