Question

Find the ratio of which X axis divides the line segment joining the points (2,-3)and(5,6) .then find the intersecting point on X axis

Answer 1

The intersecting point on x-axis is (3,0)

Answer 2

The ratio in which the x-axis divides the line segment joining the points (2,-3) and (5,6) is 1:2.

Step-by-step explanation:

We have to find the ratio of which the x-axis divides the line segment joining the points (2,-3) and (5,6).

Let the ratio in which the x-axis divides the line segment be 'k:1'.

So, let the coordinate ($x_1,y_1$) = (2, -3) and the coordinate ($x_2,y_2$) = (5, 6).

Now, the section formula is given by;

(x, y) = ( $\frac{m_1x_2+m_2x_1}{m_1+m_2} , \frac{m_1y_2+m_2y_1}{m_1+m_2}$ )

Here, $m_1 = k$ and $m_2=1$.

As it is given in the question that we have to find the ratio of which the x-axis divides the line segment and on the x-axis, y coordinate is 0, that means;

$\frac{m_1y_2+m_2y_1}{m_1+m_2}=0$

$\frac{(k \times 6)+(1 \times (-3))}{k+1}=0$

$\frac{6k-3}{k+1}=0$

$6k-3=0$

$k = \frac{3}{6}$

So, $k=\frac{1}{2}$

This means the ratio in which the x-axis divides the line segment joining the points (2,-3) and (5,6) is 1:2.

Now, the value of x-coordinate will be = $\frac{m_1x_2+m_2x_1}{m_1+m_2}$

                                                                = $\frac{(1 \times 5)+(2 \times 2)}{1+2}$

                                                                = $\frac{5+4}{3}$ = 3

Hence, the intersecting point on the x-axis is (3, 0).