HOW TO FIND THE POINTS THAT DIVIDE THE LINE SEGMENT INTO FOURTHS

About "How to find the points that divide the line segment into fourths"

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)

Related topics

• 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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