10th CBSE math solution for exercise 7.2 part 3

This page 10th CBSE math solution for exercise 7.2 part 3 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 3

(4) Find the ratio in which the line segment joining the points (-3,10) and (6,-8) is divided by (-1,6).

Solution:

Here x₁ = -3, y₁ = 10, x₂ = 6, y₂ = -8 

         [m(6) + n (-3)]/(m+n) , [m (-8) + n (10)]/(m+n) = (-1,6)

        (6m - 3n)/(m+n), (-8m+10n)/(m+n) = (-1,6)

 equating the coefficients of x and y

    (6m-3n)/(m+n) = -1       (-8m+10n)/(m+n) = 6

       6m -  3n = -1 (m+n)

     6m - 3n = -1 (m+n)

      6m-3n=-m-n

      6m+m=-n+3n

       7m=2n

        m/n= 2/7

        m:n = 2:7

So the point (-1,6) is dividing the line segment in the ratio 2:7.


(5) Find the ratio in which the line segment joining A (1,-5) and B(-4,5) is divided by the x axis.Also find the coordinates of the point of division.

Solution:

Let m:n be the ratio which divides the line segment joining the points A(1,-5) and B(-4,5)

Since the point of division is on x axis y-coordinate value will be 0.

x₁ = 1, y₁ = -5, x₂ = -4 , y₂ = 5 

    m(-4) + n(1)/(m+n) , m(5) + n(-5)/(m+n) = (x,0)

   (-4m + n) /(m+n) , (5m-5n)/(m+n) = (x,0)

  (-4m + n)/(m+n) = x      (5m - 5n)/(m+n) = 0

    (5m - 5n)/(m+n) = 0

   5 m - 5 n = 0

    5 m = 5 n

      m/n = 5/5

     m:n = 1:1

In the page 10th CBSE math solution for exercise 7.2 part 3 we are going to see the solution of next problem

 (6) If (1,2),(4,y) (x,6) and (3,5) are the vertices of a parallelogram taken in order,find x and y

Solution:

Let A(1,2),B(4,y) C(x,6) and D(3,5) are the vertices of a parallelogram.

In a parallelogram midpoint of the diagonals will be equal.

 Midpoint of diagonal AC = Midpoint of diagonal BD

    midpoint = (x₁ + x₂)/2 , (y₁ + y₂)/2

Midpoint of diagonal AC :

x₁ = 1, y₁ = 2, x₂ = x , y₂ = 6 

                  = (1+x)/2,(2+6)/2

                  = (1+x)/2,8/2

                  = (1+x)/2,4

Midpoint of diagonal BD :

x₁ = 4, y₁ = y, x₂ = 3 , y₂ = 5 

                  = (4+3)/2,(y+5)/2

                  = 7/2,(y+5)/2

(1+x)/2,4 = 7/2,(y+5)/2

(1 + x)/2 = 7/2

    1 + x = 7             4 = (y + 5)/2

    x = 7 - 1              8 = y + 5

     x = 6                  y = 8 - 5

                              y = 3




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