Section Formula Worksheet Solution4





In this page section formula worksheet solution4 we are going to see solution for each questions with detailed explanation.

(10) Find the points which divide the line segment joining A(-4,0) and B(0,6) into four equal parts

Let P,Q and R are the points of the line segment joining the line segment A and B

Here AP = PQ = QR = RB  

AP = 1

PQ = 1

QR = 1

RB = 1

Section formula internally = (Lx₂ + mx₁)/(L + m) , (Ly₂ + my₁)/(L + m)

P divides the line segment in the ratio 1:3

L = 1      m = 3  (-4,0) (0,6)    

                           = [(1x0) + (3x(-4)]/(1+3) , [(1x6) + (3x0]/(1+3)

                           = (0 - 12)/4 , (6 + 0)/4

                           =  -12/4 , 6/4

                           =  P (-3 , 3/2)

Q divides the line segment in the ratio 2:2

L = 2      m = 2    

                        = [(2x0) + (2x(-4)]/(2+2) , [(2x6) + (2x0]/(2+2)

                        = (0 - 8)/4 , (12 + 0)/4

                        =  -8/4 , 12/4

                        =  Q (-2 , 3)

R divides the line segment in the ratio 3:1

L = 3      m = 1    

                        = [(3x0) + (1x(-4)]/(3+1) , [(3x6) + (1x0]/(3+1)

                        = (0 - 4)/4 , (18 + 0)/4

                        =  -4/4 , 18/4

                        =  R (-1 , 9/2)


(11) Find the ratio in which x axis divides the line segment joining the points (6 , 4) and (1 ,- 7).

Solution:                              

Let L : m be the ratio of the line segment joining the points (6,4) and (1,-7) and let p(x,0) be the point on the x axis

Section formula internally = (Lx₂ + mx₁)/(L + m) , (Ly₂ + my₁)/(L + m)

                       (x , 0)   = [L(1) + m(6)]/(L + m) , [L(-7) + m(4)]/(L + m)

                        (x , 0)   = [L + 6 m]/(L + m) , [-7L + 4m]/(L + m)

Equating y-coordinates

         [-7L + 4m]/(L + m) = 0

                    - 7 L + 4 m = 0

                            - 7 L = - 4 m

                             L/m = 4/7

                L : m = 4 : 7              

Therefore x-axis divides the line segment in the ratio 4:7.

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