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

$A$ point both of whose coordinates are negative will lie in

Plot the points $A(1, -1)$ and $B(4, 5)$.
$(i)$ Draw a line segment joining these points. Write the coordinates of a point on this line segment between the points $A$ and $B$.
$(ii)$ Extend this line segment and write the coordinates of a point on this line which lies outside the line segment $AB$.

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.

Three vertices of a rectangle are $(3,2), (-4,2)$ and $(-4,5)$. Plot these points and find the coordinates of the fourth vertex.

In which quadrant or on which axis does each of the following points lie?
$A(10, 40), B(-30, 0), C(50, -40), D(0, -30), E(-20, 50), F(0, 60), G(70, 0), H(-40, -50)$
Verify your answer by plotting the points in the Cartesian plane. Use the scale $1 \, cm = 10$ units on both axes.