Question

From the figure, find the ratio in which the line segment joining the points A(3, 4) and C(9, 4) is divided by x = 5.

• A. 1:1
• B. 2:1
• C. 1:2
• D. 3:1

Answer 1

The correct option is C 1:2

Let $O(5,y)$ divide $AB$ in the ratio $k:1$.

By section formula, the coordinates of $O$ are given by: $(\frac{9k+3}{k+1},\frac{4k+4}{k+1})$

But $O(5,y)=(\frac{9k+3}{k+1},\frac{4k+4}{k+1})$ $\Rightarrow \frac{9k+3}{k+1}=5$

$\Rightarrow 9k+3$ = 5k+5
$\Rightarrow 4k$ = 2
$\Rightarrow k$ = $\frac{1}{2}$

i.e., the line x = 5 divides $AB$ in the ratio $1:2$.