Question

Find the ratio in which the point (2, a) divides the joining of (-4, 3) and (6, 3). Hence, find a.
[4 MARKS]

Answer 1

Formula: 1 Mark
Steps: 1 Mark
Ratio: 1 Mark
Value of $a$: 1 Mark

Let the point (2, a) divide the line segment joining (-4, 3) and (6, 3) in the ratio k:1.
Using section formula, we have
$2=\frac{6k-4}{k+1}\Rightarrow 4k=6\Rightarrow k=\frac{3}{2}$
$\therefore$ Point (2, a) divides the joining of (-4, 3) and (6, 3) in the ratio 3 : 2
and $a=\frac{3k+3}{k+1}$
Putting $k=\frac{3}{2}$, we get
$a=\frac{\frac{9}{2}+3}{\frac{3}{2}+1}=3$