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)
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