Question

In what ratio is the join of (4.3) and (2,-6)
divided by the x-axis ? Also, find the
co-ordinates of the point of intersection.
1​

Answer 1

We have:-

• Coordinates of points (4,3) and (2,-6)
• It is divided by x axis.

To FinD:-

• Coordinates of the point of intersection.
• Ratio in which it is divided?

Explanation:-

By using section formula:

Consider two points P(x1, y1) and Q(x2, y2). We have to find the coordinates of the point R which divides PQ in the ratio m : n,

$\boxed{\rm{x = \frac{mx2 + nx1}{m + n} }} \: \boxed{ \rm{y = \frac{my2 + ny1}{m + n}}}$

Here,

• x1 = 4
• y1 = 3
• x2 = 2
• y2 = -6

Let the ratio be k : 1.

As we can see that, the ordinate or y-coordinate = 0. Equating to 0, for getting k:

$\rm{0 = \dfrac{k \times - 6 + 1 \times 3}{k + 1} }$

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

Then,

$\rm{ - 6k + 3 = 0}$

$\rm{ - 6k = - 3}$

$\rm{k = \dfrac{1}{2} }$

The required ratio is k : 1 = 1 : 2

Now putting the value for finding the x-coordinate,

We have,

$\rm{x = \dfrac{2k + 4}{k + 1} }$

$\rm{x = \dfrac{2 \times \frac{1}{2} + 4}{ \frac{1}{2} + 1} }$

$\rm{ x= \dfrac{1 + 4}{ \frac{3}{2} } }$

$\rm{x = \dfrac{10}{3} }$

Hence:-

• The ratio in which x- axis divides the line is 1 : 2

• The coordinates of the points on x-axis is (10/3, 0)