Section Formula Worksheet Solution3





In this page section formula worksheet solution3 we are going to see solution for each questions with detailed explanation.

(7) Find the coordinates of the point which divides the line segment joining (-3 ,5) and (4 , -9) in the ratio 1:6 internally.

Solution:

Let  A (-3 , 5) and B (4 , -9)

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

L = 1      m = 6    

                     = [(1x4) + (6x(-3)]/(1+6) , [(1x(-9)) + (6x5)]/(1+6)

                     = (4-18)/7 , (-9 + 30)/7

                     =  -14/7 , 21/7

                     = (- 2 , 3) 


(8) Let A (-6 , -5) and B(-6 , 4) be the two points such that a point  P on the line AB satisfies AP = (2/9) AB. Find the point P.

Solution:

AP = (2/9) AB

9 AP = 2 (AP+PB)

9 AP = 2 AP + 2 PB

9 AP – 2 AP = 2 PB

7 AP = 2 PB

AP/AB = 2/7

AP: PB = 2: 7

So P divides the line segment in the ratio 2:7

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

L = 2      m = 7    

                        = [(2x(-6)) + (7x(-6)]/(2+7) , [(2x(4)) + (7x(-5)]/(2+7)

                        = (-12-42)/9 , (8 - 35)/9

                        =  -54/9 , -21/7

                        =  (-6 , -3)


(9) Find the points of trisection of the line segment joining the points A (2 , -2) and B (-7 , 4).

Solution:

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

Here AP = PQ = QB   

 AP = 1

PQ = 1

QB = 1

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

P divides the line segment in the ratio 1:2

L = 1      m = 2    

                          = [(1x(-7)) + (2x2)]/(1+2) , [(1x4) + (2x(-2)]/(1+2)

                          = (-7 + 4)/3 , (4 - 4)/3

                          =  -3/3 , 0/3

                          =  P (-1 , 0)

Q divides the line segment in the ratio 2:1

L = 2      m = 1    

                          = [(2x(-7)) + (1x2)]/(2+1) , [(2x4) + (1x(-2)]/(2+1)

                          = (-14 + 2)/3 , (8 - 2)/3

                          =  -12/3 , 6/3

                          =  Q (-4 , 2)

section formula worksheet solution3  section formula worksheet solution3