**How to find the points that divide the line segment into fourths :**

Here we are going to see how to find the points that divide the line segment into fourths.

Let us look into some examples to understand the above concept.

**Example 1 :**

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

**Solution :**

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

Here AP = PQ = QR = RB

If AP = 1, PQ = 1, QR = 1 and 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 A (-4,0) and B (0,6)

= [1(0) + 3(-4)]/(1+3) , [1(6) + 3(0)]/(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

= [2(0) + 2(-4)]/(2+2) , [2(6) + 2(0)]/(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

= [3(0) + 1(-4)]/(3+1) , [3(6) + 1(0)]/(3+1)

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

= -4/4 , 18/4

= R (-1 , 9/2)

Hence the points divides the line segment into four parts are P (-3 , 3/2), Q (-2 , 3) and R (-1 , 9/2)

- Find the coordinates of the point that divides the line segment into three parts
- How to find the ratio in which a point divides a line
- Midpoint of the line segment
- Section formula
- How to find the missing coordinate of a parallelogram

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