Question

In what ratio, does the $x-axis$ divides the line segment joining the points (2, -3) and (5, 6)? [4 MARKS]

Answer 1

Formula: 1 Mark
Steps: 2 Marks
Answer: 1 Mark

Let x-axis cuts the line segment joining the points A (2, -3) and B(5, 6) at (a, 0) and the x-axis divides the line segment AB in the ratio $k:1$.
Using section formula, we have
$0=\frac{k\times 6+1\times (-3)}{k+1}\Rightarrow 6k=3\Rightarrow k=\frac{1}{2}$
$\therefore$ $x-axis$ divides it in the ratio 1 : 2