Question

Find the ratio in which the x-axis divides internally the line joining points A (6, -4) and B ( -3, 8).​

Answer 1

the ratio is 1:2 and the division is internal.

Answer 2

Given:

The x-axis divides internally the line joining points A (6, -4) and B ( -3, 8).

To find:

The ratio in which the x-axis divides internally the line joining points A (6, -4) and B ( -3, 8).

Solution:

The ratio in which the x-axis divides the line joining the given points A and B internally is 1:2.

To answer this question, we will follow the following points:

First of all, we should know that if a line joining two points A(p, q) and B(a, b) is divided internally by another line in the ratio m:n at C having coordinates (x, y), then the point (x, y) is given by:

$x = \frac{m(a) + n(p)}{m + n} \: \: (i)$

and

$y = \frac{m(b) + n(q)}{m + n} \: \: (ii)$

Now,

As given, we have,

Two points A (6, -4) and B ( -3, 8) that is divided internally by the x-axis. So, the coordinates of a point that cuts A and B is (x, 0). This is because, at the x-axis, y = 0.

So,

Using (ii), we get

$0 = \frac{m(8) + n( - 4)}{m + n}$

$0 = 8m - 4n$

$4n = 8m$

$\frac{m}{n} = \frac{1}{2}$

Hence, the ratio in which the x-axis divides the line joining the points A (6, -4) and B ( -3, 8) internally is 1:2.