Dr. SK Goyal Solutions for Chapter: Coordinate Systems and Coordinates, Exercise 8: Multiple Choice II

Two consecutive vertices of a rectangle of area $10 {\mathrm{unit}}^2$ are $\left(1,3\right)$ and $\left(-2,-1\right)$. Other two vertices are:

If each of the vertices of a triangle has integral co-ordinates then the triangle may be:

The triangle $OAB$ is right angled where points $O,A,B$ are $\left(0,0\right),\left(\cos \theta ,\sin \theta \right)$ and $\left(\cos \varphi ,\sin \varphi \right)$ respectively, then $\theta$ and $\varphi$ are connected by the relation :

$ABC$ is an isosceles triangle. If the co-ordinates of the base are $B\left(1,3\right)$ and $C\left(-2,7\right)$. The co-ordinates of vertex $A$ can be:

If $A\left(a,a\right), B\left(-a,-a\right)$ are two vertices of an equilateral triangle, then its third vertex is:

The medians $\mathrm{AD}$ and $BE$ of the triangle with vertices $A\left(0, b\right), B\left(0,0\right)$ and $C\left(a, 0\right)$ are mutually perpendicular if :

The points $A\left(x, y\right), B\left(y, z\right)$ and $C\left(z, x\right)$ represents the vertices of a right angled triangle, if :

Let the base of a triangle lie along the line $x=a$ and be of length $2a$. The area of this triangle is $a^2$, if the vertex lies on the line :