Write the coordinates of the vertices of a rectangle which is $6$ units long and $4$ units wide if the rectangle is in the first quadrant, its longer side lies on the x-axis and one vertex is at the origin.

Write the coordinates of the vertices of a rectangle which is $6$ units long and $4$ units wide if the rectangle is in the third quadrant, its longer side lies on the x-axis and one vertex is at the origin.

In the below figure, $ABCD$ is a rectangle with length $6$ units and breadth $3$ units. If $O$ is mid-point of $AB$, find the coordinates of $A, B, C, \& D$.

In the below figure, $△PQR$ is equilateral. If the coordinates of the points $Q \& R$ are $\left(0, 2\right) \& \left(0, -2\right)$ respectively, find the coordinates of the point $P$.

The below figure shows an equilateral triangle $OAB$ with each side $2a$ units. Find the coordinates of the vertices.

Plot the points $\left(5, 0\right), \left(0, 5\right), \left(2, 5\right), \left(5, 2\right), \left(-3, 5\right), \left(-3, -5\right) \& \left(6, 1\right)$ in the Cartesian plane.

In which quadrant or on which axis do each of the points $\left(-2, 4\right), \left(3,-1\right),\left(-1, 0\right), \left(1, 2\right) \& \left(-3, -5\right)$ lie? Verify your answer by locating them on the Cartesian plane.

Taking $0.5 cm$ as $1$ unit, plot the following points on the graph paper.

$A\left(1,3\right), B\left(-3, -1\right), C\left(1, -4\right), D\left(-2, 3\right), E\left(0, -8\right) \& F\left(1, 0\right)$

Plot the following points and check whether they are collinear or not:

$\left(-1,0\right), \left(0, 1\right) \& \left(2, 3\right)$