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 $AB$.

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.

Points $A(5,3), B(-2,3)$ and $D(5,-4)$ are three vertices of a square $A B C D .$ Plot these points on a graph paper and hence find the coordinates of the vertex $C.$

In which quadrant does a point lie if its $x$ -coordinate is negative and the $y$ -coordinate is positive ?

The line joining $A (3,-8)$ and $B(3,5)$ intersects the $x$ -axis at $\ldots \ldots . .$