Question
The points $$\left( { - a, - b} \right),\left( {0,\,0} \right),\left( {a,\,b} \right)$$ and $$\left( {{a^2},\,ab} \right)$$ are :
A.
Collinear
B.
Vertices of a parallelogram
C.
Vertices of a rectangle
D.
None of these
Answer :
Collinear
Solution :
The given points are $$A\left( { - a, - b} \right),\,B\left( {0,\,0} \right),\,C\left( {a,\,b} \right){\text{ and }}D\left( {{a^2},\,ab} \right)$$
$$\eqalign{
& {\text{Slope of }}AB = \frac{b}{a} = {\text{ slope of }}BC = {\text{ slope of }}BD \cr
& \therefore A,\,B,\,C,\,D\,\,\,{\text{are collinear}}{\text{.}} \cr} $$