Which axis passes through the point $\left(7 \frac{3}{4}, 0\right)?$

Plot the point $P(-6, 2)$ and from it draw $PM$ and $PN$ as perpendiculars to the $x$-axis and $y$-axis,respectively. Write the coordinates of the points $M$ and $N$.

In which quadrant or on which axis does each of the following points lie?
$A(5, 0), B(3, -2), C(-2, 5), D(0, 4), E(-3, -4), F(4, 3), G(0, -4), H(-5, 0)$
Verify your answer by locating them on the Cartesian plane.

On plotting the points $O(0,0), A(3,0), B(3,4)$,and $C(0,4)$ and joining $OA, AB, BC$,and $CO$,which of the following figures is obtained?

State whether the following statement is true or false:
Coordinate axes intersect at $(0,0)$.

Write the coordinates of the vertices of a rectangle whose length and breadth are $5$ and $3$ units respectively,one vertex is at the origin,the longer side lies on the $x$-axis,and one of the vertices lies in the third quadrant.