Question

From the figure, find the ratio in which the line segment joining the points B(6, 7) and D(6, 1) is divided by y = 4.

• A. 1:1
• B. 1:2
• C. 2:1
• D. 3:2

Answer 1

The correct option is A 1:1

Let $P(x,4)$ divide $AB$ in the ratio $k:1$.

By section formula, the coordinates of $P$ are given by: $(\frac{6k+6}{k+1},\frac{k+7}{k+1})$

But $P(x,4)=(\frac{6k+6}{k+1},\frac{k+7}{k+1})$ $\Rightarrow \frac{k+7}{k+1}=4$

$\Rightarrow k+7$ = 4k+4
$\Rightarrow 3k$ = 3
$\Rightarrow k$ = $\frac{1}{1}$

i.e., the line y = 4 divides $AB$ in the ratio $1:1$.