The ratio in which the line segment joining the points (1,

Question

The ratio in which the line segment joining the points (1, – 7) and (6, 4) is divided by x-axis is _____.

Options:

A . 3:1

B . 2:3

C . 7:2

D . 7:4

Answer: Option D
:
D

Let $C (x, 0)$ divide $A B$ in the ratio $k : 1$ .

By section formula, the coordinates of $C$ are given by: $(\frac{6 k + 1}{k + 1}, \frac{4 k - 7}{k + 1})$

But $C (x, 0) = (\frac{6 k + 1}{k + 1}, \frac{4 k - 7}{k + 1})$ $\Rightarrow \frac{4 k - 7}{k + 1} = 0$

$\Rightarrow 4 k - 7$ = 0 $\Rightarrow k$ = $\frac{7}{4}$

i.e., the x-axis divides $A B$ in the ratio $7 : 4$ .

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