Find the ratio in which the lines segment joining A(1,-5) & B(-4,5) is divided by the x-axis. Also find the corrdinates of the point of the division.

Step-by-step explanation:

Given that

A line segment AB having coordinates of A as (1, - 5) and coordinates of B as (- 4, 5).

Let assume that x - axis divides the line segment joining the points A (1, - 5) and B (- 4, 5) in the ratio k : 1 at C.

Let assume that coordinates of C be (x, 0).

We know,

Section formula :-

Let P(x₁, y₁) and Q(x₂, y₂) be two points in the coordinate plane and R(x, y) be the point which divides PQ internally in the ratio m₁ : m₂. Then, the coordinates of R will be:

So, on substituting the values, we get

On comparing y - coordinate on both sides, we get

Hence,

The x - axis divides the line segment joining the points A (1, - 5) and B (- 4, 5) in the ratio 1 : 1 at C.

Now, On comparing x - coordinate on both sides, we get

On substituting the value of k, we get

Hence,

The coordinates of point of intersection, C is

by definition, an arc subtended by a central angle of some given measure has the same measure. so .