Question 15 Marks

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 $AB.$

Answer

In point $A(1, -1), x-$coordinate is positive and $y-$coordinate is negative, so it lies in $IV$ quadrant.
In point $B(4, 5),$ both coordinates are positive, so it lies in $I$ quadrant.
On plotting these point, we get the following graph.

$i.$ On joining the points $A$ and $B,$ we get the line segment $AB.$
Now, to find the coordinates of a point on this line segment between $A$ and $B$ draw a perpendicular to $X-$axis from $x = 2$ and $3. [$since, $x = 2$ and $3$ lies between $A$ and $B]$ say it intersect line segment $AB$ at $P$ and $p\ ’.$
Now, draw a perpendicular to $Y-$axis from $P$ and $p\ ’,$ they intersect $Y$ axis at $y = 1$ and $3,$ respectively.
Thus, we get points $(2,1)$ and $(3, 3)$ which lie between line segment $AB.$
$ii.$ Extent the line segment $AB.$ 
Now, draw a perpendicular to $X-$axis from $x = 5,$ say it intersects extended line segment at $Q.$
Again, draw a perpendicular to $Y-$axis from $Q$ and it intersects $Y-$axis at $y = 7$.
Thus, we get the point $Q(5,7)$ which lies outside the line segment $AB.$

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