Q. 34.6( 5 Votes )

Let us write by calculating what value of K, the points (1, –1), (2, –1) and (K, –1) lie on same straight line.

Answer :

Let the points be


A = (x1, y1) = (1, -1) and


B = (x2, y2) = (2, -1) and


C = (x3, y3) = (K, -1)


These points lie on a straight line which means points A, B and C are collinear


As these points are collinear the area of triangle formed by these points would be 0


Area = 0


Area of triangle is given by formula


Area = × [x1(y2 – y3) + x2(y3 – y1) + x3(y1 – y2)]


Where (x1, y1), (x2, y2) and (x3, y3) are vertices of triangle


× [x1(y2 – y3) + x2(y3 – y1) + x3(y1 – y2)] = 0


× [1(-1 – (-1)) + 2(-1 – (-1)) + K(-1 – (-1))] = 0


× [1(-1 + 1) + 2(-1 + 1) + K(-1 + 1)] = 0


K × 0 = 0 … (a)


Here we can put any value for K from negative infinity to infinity and our equation (a) is satisfied


Hence K can take any value for the points (1, –1), (2, –1) and (K, –1) to lie on same straight line.


Method 2


If we plot the given points we can observe that K can take any value since the y-coordinate for all the points A, B and C is the same



Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Champ Quiz |  2-Dimension( Coordinate geometry )Champ Quiz |  2-Dimension( Coordinate geometry )Champ Quiz | 2-Dimension( Coordinate geometry )36 mins
Basic Understanding of Coordinate GeometryBasic Understanding of Coordinate GeometryBasic Understanding of Coordinate Geometry33 mins
Champ Quiz | Area of TriangleChamp Quiz | Area of TriangleChamp Quiz | Area of Triangle53 mins
Basics of Coordinate GeometryBasics of Coordinate GeometryBasics of Coordinate Geometry43 mins
Champ Quiz | Area of ParallelogramChamp Quiz | Area of ParallelogramChamp Quiz | Area of Parallelogram55 mins
Quiz | Imp. Qs. on Coordinate GeometryQuiz | Imp. Qs. on Coordinate GeometryQuiz | Imp. Qs. on Coordinate Geometry39 mins
Know How to Solve Complex Geometry Problems!Know How to Solve Complex Geometry Problems!Know How to Solve Complex Geometry Problems!27 mins
Coordinate GeometryCoordinate GeometryCoordinate Geometry45 mins
Quiz | Area and ParallelogramQuiz | Area and ParallelogramQuiz | Area and Parallelogram46 mins
Euclid's GeometryEuclid's GeometryEuclid's Geometry51 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
caricature
view all courses