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.

section formula worksheet solution4 section formula worksheet solution4

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