Aspire's Library
A Place for Latest Exam wise Questions, Videos, Previous Year Papers,
Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
The points $(K,2-2K)$, $(-K+1,2K)$ and $(-4-K,6-2K)$ are collinear if:
(A) $K=\frac{1}{2}$
(B) $K=\frac{-1}{2}$
(C) $K=\frac{3}{2}$
(D) $K=-1$
(E) $K=1$
Choose the correct answer from the options given below:
Solution
Given points:
\[
P_1(K,2-2K), \quad P_2(1-K,2K), \quad P_3(-4-K,6-2K)
\]
These three points are collinear if the area of triangle formed by them is zero:
\[
\Delta =
\begin{vmatrix}
K & 2-2K & 1\\
1-K & 2K & 1\\
-4-K & 6-2K & 1
\end{vmatrix} = 0
\]
Expanding determinant:
\[
8K^2 + 4K - 4 = 0 \;\;\Rightarrow\;\; 2K^2 + K - 1 = 0
\]
Solving quadratic:
\[
K = \frac{-1 \pm 3}{4} \;\;\Rightarrow\;\; K=\tfrac{1}{2},\; -1
\]
Online Test Series, Information About Examination,
Syllabus, Notification
and More.
View More
Online Test Series, Information About Examination,
Syllabus, Notification
and More.
View More
Ask Your Question or Put Your Review.
