This page 10th CBSE math solution for exercise 7.2 part 2 is going to provide you solution for every problems that you find in the exercise no 7.2

(1) Find the coordinates of the point which divides the join of (-1,7) and (4,-3) in the ratio 2 : 3.

Solution:

Here x₁ = -1, y₁ = 7, x₂ = 4 , y₂ = -3 m = 2 and n = 3

= [2 (4) + 3 (-1)]/(2+3) , [2 (-3) + 3 (7)]/(2+3)

= (8 - 3)/5, (-6+21)/5

= 5/5, 15/5

= (1,3)

(2) Find the coordinates of the points of trisection of the line segment joining (4,-1) and (-2,-3).

Solution:

Let "C" and "D" be the points which divides the line segment into three equal parts.

length of AC = 1 unit

length of CD = 1 unit

length of DB = 1 unit

So C divides the line segment in the ratio 1 : 2

x₁ = 4, y₁ = -1, x₂ = -2 , y₂ = -3 m = 1 and n = 2

= [1 (-2) + 2 (4)]/(1+2) , [1 (-3) + 2 (-1)]/(1+2)

= (-2 + 8)/3, (-3-2)/3

= 6/3, -5/3

= (2,-5/3)

So D divides the line segment in the ratio 2 : 1

x₁ = 4, y₁ = -1, x₂ = -2 , y₂ = -3 m = 2 and n = 1

= [2 (-2) + 1 (4)]/(2+1) , [2 (-3) + 1 (-1)]/(2+1)

= (-4 + 4)/3, (-6-1)/3

= 0/3, -7/3

= (0,-7/3)

In the page 10th CBSE math solution for exercise 7.2 part 2 we are going to see the solution of next problem

(3) To conduct sports day activitie,in your rectangular shaped school ground ABCD, lines have been drawn which 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 7.12. Niharika runs ¼ th the distance AD on the second line and posts a green flag. Preet runs 1/5th the distance AD on the eight line and posts a red flag. What is 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?

Solution:

It can be observed that Naharika posted a green flag at 1/4 th of the distance AD (1/4) x 100 = 25 m from the starting point of the 2nd line. Therefore the coordinates of the point is (2,25)

Similarly Preet post red flag at 1/5th of the distance AD .(1/5)x100=20mfrom the starting point of the 8th line.Therefore, the coordinates of this point R are (8,20). Distance between these flags by using distance formula GR

= **√(x₂ - x₁)² + (y₂ - y₁)****²**

= **√(8 - 2)² + (20 - 25)****²**

= **√6² + (-5)****²**

= **√36 + 25**

= **√61 m**

**The point at which Rashmi should post her blue flag is the midpoint of the line joining these points.**

** x = (8 + 2)/2 , y = (25 + 20)/2**

** = 10/2 , 45/2**

** = (5,22.5)**

**Therefore Rashmi should post her flag at 22.5m on 5th line.**

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