Identification of Collinear Points


Coordinate Geometry II - Concepts
Class - 10th NTSE Subjects
 
 
Concept Explanation
 

Identification of Collinear Points

Collinearity: 

All the points that lie on the same straight line are said to be colinear points.

Identification of Collinear Points

There are two method to check whether the three points are colinear or not

1. Slope Method

2. Area method

1 Slope Method:

Three or more points are collinear, if slope of any two pairs of points is same. To check whether the the points are colinear we will find the slope of any two pair of points and if the slope is equal the three points are said to be colinear. With three points A(x_{1},y_{1}),B(x_{2},y_{2}) and C(x_{3},y_{3}), three pairs of points can be formed, they are: AB, BC and AC. If Slope of AB = Slope of BC = Slope of AC, then A, B and C are collinear points.

Formula for the slope between two points A(x_{1},y_{1}),B(x_{2},y_{2}) is

Slope ;of; AB = frac{y_2-y_1}{x_2-x_1}

For the points to be colinear the condition is

Slope of AB = Slope of BC

frac{y_2-y_1}{x_2-x_1} = frac{y_3-y_2}{x_3-x_2}

2. Area Method:

Three points A(x_{1},y_{1}),B(x_{2},y_{2})  and  C(x_{3},y_{3}) will be collinear if and only if area of triangle ABC is zero, that is, if and only if,

  frac{1}{2}left | x_{1}(y_{2}-y_{3})+x_{2}(y_{3}-y_{1})+x_{3}(y_{1}-y_{2}) right |=0

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Sample Questions
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Question : 1

 Given that the points P (8, 1), Q (15, 7), and R (x, 3) are collinear. Find x.

Right Option : C
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Question : 2

Which is the correct terms for points that  do not lie on the same line ?

Right Option : C
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Question : 3

________________ Points are points that lie on the same line .

Right Option : B
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