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

3 answers
Question:

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.

Answers

Step-by-step explanation:

[tex]\large\underline{\sf{Solution-}}[/tex]

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:

[tex]\sf\implies \boxed{\tt{ R = \bigg(\dfrac{m_{1}x_{2}+m_{2}x_{1}}{m_{1}+m_{2}}, \dfrac{m_{1}y_{2}+m_{2}y_{1}}{m_{1}+m_{2}}\bigg)}}[/tex]

So, on substituting the values, we get

[tex]\rm \longmapsto\:(x,0) = \bigg(\dfrac{ - 4k + 1}{k + 1}, \: \dfrac{5k - 5}{k + 1} \bigg)[/tex]

On comparing y - coordinate on both sides, we get

[tex]\rm \longmapsto\:\dfrac{5k - 5}{k + 1} = 0[/tex]

[tex]\rm \longmapsto\:5k - 5 = 0[/tex]

[tex]\rm \longmapsto\:5k = 5[/tex]

[tex]\bf\implies \:k = 1[/tex]

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

[tex]\rm \longmapsto\:x = \dfrac{ - 4k + 1}{k + 1}[/tex]

On substituting the value of k, we get

[tex]\rm \longmapsto\:x = \dfrac{ - 4+ 1}{1 + 1}[/tex]

[tex]\rm \longmapsto\:x \: = - \: \dfrac{3}{2}[/tex]

Hence,

The coordinates of point of intersection, C is

[tex]\rm\implies \:\boxed{\tt{ Coordinates \: of \: C = \bigg( - \dfrac{3}{2}, \: 0 \bigg) }}[/tex]

step-by-step explanation:

a mantle plume is an upwelling of abnormally hot rock within the earth's mantle. as the heads of mantle plumes can partly melt when they reach shallow depths, they are thought to be the cause of volcanic centers known as hotspots and probably also to have caused flood basalts.

step-by-step explanation:

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