R S Aggarwal and Veena Aggarwal Solutions for Exercise 4: MULTIPLE-CHOICE QUESTIONS (MCQ)

Two vertices of $△ABC$ are $A\left(-1, 4\right)$ and $B\left(5, 2\right)$ and its centroid is $G\left(0, -3\right)$. Then, the coordinates of the third vertex are 

The points $\mathrm{A}\left(-4, 0\right), \mathrm{B}\left(4, 0\right)$ and $\mathrm{C}\left(0, 3\right)$ are the vertices of a triangle, which is (Isosceles/Scalene/Equilateral)

The point $P\left(0, 6\right), Q\left(-5, 3\right)$ and $R\left(3, 1\right)$ are the vertices of a triangle, which is 

If the points $A\left(2, 3\right), B\left(5, k\right)$ and $C\left(6, 7\right)$ are collinear then 

If the point $A\left(1, 2\right), O\left(0, 0\right)$ and $C\left(a, b\right)$ are collinear then

The area of $∆ABC$ with vertices $A\left(3, 0\right), B\left(7, 0\right)$ and $C\left(8, 4\right)$ is

$AOBC$ is a rectangle whose three vertices are $A\left(0,3\right),O\left(0,0\right)$ and $B\left(5,0\right).$ The length of its diagonal is

If the distance between the points $A\left(4, p\right)$ and $B\left(1, 0\right)$ is $5$ then