The ratio in which the x-axis divides the line segment joining the points (2, –3) and (6, 7) is:

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Solution

Q.
The ratio in which the x-axis divides the line segment joining the points (2, –3) and (6, 7) is:

1 1 : 3

2 3 : 7

3 7 : 3

4 1 : 2

Ans.
(2)

Let P(x, 0) be a point on the x-axis such that it divides the line segment joining
A(2, –3) and B(6, 7) in the ratio k : 1.

Using the section formula, we get:

$y = \frac{k y_{2} + y_{1}}{k + 1} 0 = \frac{k \times 7 + 1 \times (- 3)}{k + 1} 0 = 7 k - 3 \Rightarrow k = \frac{3}{7} S o, t h e r a t i o i s : \frac{3}{7} : 1 i . e ., 3 : 7$

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