Trisection Points of Line


Coordinate Geometry I - Concepts
Class - 10th IMO Subjects
 
 
Concept Explanation
 

Trisection Points of Line

Trisection means dividing a line segment into three equal parts.

To divide a line segment AB into three equal parts we have to find two points P and Q such that AP = PQ= QB

Let AP = PQ = QB = k

Then AP = k and PB = PQ + QB = k + k=2k

That means P divides the line segment in the ratio k : 2k = 1 : 2

The coordinates of ;P(x_3,y_3) can be found by using the section formula for coordinates A(x_1,y_1) and B(x_2,y_2) using the ration 1:2

x_3=frac{1(x_2)+2(x_1)}{1+2};and; y_3=frac{1(y_2)+2(y_1)}{1+2}

x_3=frac{x_2+2x_1}{3};and; y_3=frac{y_2+2y_1}{3}

Similarly, AQ = AP + PQ = k + k = 2k and QB = k

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Sample Questions
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Question : 1

Find the coordinates of the points of trisection of the line segment joining (4, -1) and (1, -3).

Right Option : B
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Question : 2

In the given figure P(6,-3) and Q(2,y) are the points of trisection of the line segment joining A(7,-2) and B(1,-5). Then, y equals : 

Right Option : A
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Question : 3

In trisection we divide a line segment into  _____________ parts . 

Right Option : C
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