10th CBSE math solution for exercise 7.2 part 1

This page 10th CBSE math solution for exercise 7.2 part 1 is going to provide you solution for every problems that you find in the exercise no 7.2

10th CBSE math solution for exercise 7.2 part 1

(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 1 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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