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 $AB$.

(N/A) The equation of the line passing through $A(1, -1)$ and $B(4, 5)$ is given by the slope-intercept form.
Slope $m = \frac{5 - (-1)}{4 - 1} = \frac{6}{3} = 2$.
Using point-slope form: $y - (-1) = 2(x - 1) \implies y + 1 = 2x - 2 \implies y = 2x - 3$.
$(i)$ To find a point between $A$ and $B$,we can choose an $x$-coordinate between $1$ and $4$. Let $x = 2$. Then $y = 2(2) - 3 = 1$. Thus,$M(2, 1)$ is a point on the line segment $AB$.
$(ii)$ To find a point outside the line segment $AB$,we can choose an $x$-coordinate greater than $4$ or less than $1$. Let $x = 5$. Then $y = 2(5) - 3 = 7$. Thus,$N(5, 7)$ is a point on the line which lies outside the line segment $AB$.