wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Find the value of k if points A(k, 3), B(6, −2) and C(−3, 4) are collinear.

Open in App
Solution

The formula for the area ‘A’ encompassed by three points, and is given by the formula,
=12x1y2+x2y3+x3y1-x2y1+x3y2+x1y3

If three points are collinear the area encompassed by them is equal to 0.

The three given points are A(k, 3), B(6, −2) and C(−3, 4). It is also said that they are collinear and hence the area enclosed by them should be 0.
=12k-2+6×4+-3×3-6×3+-3-2+k×4 0=12-2k+24-9-18+6+4k 0=12-2k+15-24-4k 0=12-6k-9 0=-6k-9 k=-96=-32

Hence the value of ‘k’ for which the given points are collinear is.


flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Basic Concepts
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon