Coordinate Geometry Question 37
Question: The points $ (-a,-b),\ (0,0),\ (a,b) $ and $ (a^{2},ab) $ are
[IIT 1979]
Options:
A) Collinear
B) Vertices of a rectangle
C) Vertices of a parallelogram
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
Here area of quadrilateral is equal to area of $ \Delta ABD $ +area of $ \Delta BCD $
$ = \begin{vmatrix} -a & -b & 1 \\ 0 & 0 & 1 \\ a^{2} & ab & 1 \\ \end{vmatrix} + \begin{vmatrix} 0 & 0 & 1 \\ a & b & 1 \\ a^{2} & ab & 1 \\ \end{vmatrix} =0 $
Hence the points are collinear.
BETA
