Q. 7 B5.0( 1 Vote )

Using distance formula, examine whether the following sets of points are collinear?(5, 1), (1, - 1), (11, 4)

Given points are A(5, 1), B(1, - 1) and C(11, 4).

We need to check whether these points are collinear.

We know that for three points A, B and C to be collinear, the criteria to be satisfied is a linear relationship between AB, BC and AC.

Let us find the distances first,

We know that distance between two points (x1, y1) and (x2, y2) is

AC = 3√5 ..... (1)

AB = 2√5 ..... (2)

BC = 5√5 ..... (3)

From (1), (2), (3) we can see that AB + AC = BC.

The three points are collinear.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Some Interesting Proofs in Geometry36 mins
Section Formula30 mins
Previous Year RMO Questions43 mins
NCERT | Most Important Proofs for Boards28 mins
Know About Important Proofs in Triangles33 mins
Measuring distance by Distance formula49 mins
Champ Quiz | Previous Year NTSE Questions29 mins
Smart Revision | Become a Master in Coordinate Geometry54 mins
Distance Formula and Section Formula44 mins
NCERT | Quiz on Section Formula43 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses