Straight Line and Pair of Straight Lines 1 Question 40
40. The points $(-a,-b),(0,0),(a, b)$ and $\left(a^{2}, a^{3}\right)$ are
(a) collinear
(b) vertices of a rectangle
$(1979,2 M)$
(c) vertices of a parallelogram
(d) None of the above
Objective Questions II
(One or more than one correct option)
Show Answer
Solution:
- The point $O(0,0)$ is the mid-point of $A(-a,-b)$ and $B(a, b)$. Therefore, $A, O, B$ are collinear and equation of line $A O B$ is
$$ y=\frac{b}{a} x $$
Since, the fourth point $D\left(a^{2}, a b\right)$ satisfies the above equation.
Hence, the four points are collinear.
