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Step-by-step explanation:
<u>Given that </u>
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
<u>Hence, </u>
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
<u>Hence, </u>
The coordinates of point of intersection, C is