Q. 194.6( 7 Votes )

Find the value of k, if the points A (8, 1), B (3, - 4) and C (2, k) are collinear.

Answer :

Given points are A(8,1),B(3,−4) and C(2,k).It is also said that they are collinear and hence the area enclosed by them should be 0.


Area of the triangle having vertices (x1,y1), (x2,y2) and (x3,y3)


= |x1(y2-y3)+x2(y3-y1)+x3(y1-y2)|


Given that area of ∆ABC = 0


0 = |8(-4 – k) + 3(k – 1) + 2(1 – (-4))|


0 = |-32 – 8k + 3k -3 + 10|


5k + 25 = 0


k = -5


Hence, the value of k is -5.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Chemical Co-ordination VS Neural Co-ordination48 mins
Section Formula30 mins
Quiz | Chemical Co-ordination47 mins
Quiz | Neural Co-ordinataion51 mins
Previous Year RMO Questions43 mins
NCERT | Most Important Proofs for Boards28 mins
Know About Important Proofs in Triangles33 mins
Champ Quiz | Previous Year NTSE QuestionsFREE Class
Measuring distance by Distance formula49 mins
Foundation | Human Endocrine System58 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