HOW TO SHOW THE GIVEN POINTS ARE COLLINEAR USING SECTION FORMULA

If three points are collinear, then one of the points divide the line segment joining the other two points in the ratio r : 1.

The section formula can be used only when the given three points are collinear.

Example :

Using section formula, show that the points A (7, −5), B (9, −3) and C (13, 1) are collinear.

Solution :

Section formula  =  (mx₂+nx₁) / (m+n),  (my₂+ny₁) / (m+n)

Let the point B divides the line segment joining the point A and C in the ratio k : 1

k (13) + 1 (7) / (k + 1), k (1) + 1 (-5) / (k + 1)  =  (9, -3)

(13k + 7)/(k + 1), (k - 5) / (k + 1)  =  (9, -3)

Equating the x and y coordinates

We get the same values for k, hence the point A, B and C are collinear.

Related topics

• Finding distance between two points worksheet
• Distance between two points word problems
• Using Pythagorean theorem to find distance between two points
• How to determine if points are collinear using distance formula
• Conditions for collinear points
• Naming collinear and coplanar points
• How to Check if Given Four Points Form a Square 
• How to Check if Given Four Points Form a Rectangle
  
• How to Check If the Given Points Form a Parallelogram
  
• How to Check if the Given Four Points Form a Rhombus
  
• Show That the Points are the Vertices of a Right Triangle
  

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