Question

The ratio in which x - axis divides the line segment joining the points (5, 4) and (2. -3) is:

Answer 1

Step-by-step explanation:

Given :-

The points are (5, 4) and (2, -3)

To find :-

Find the ratio in which x - axis divides the line segment joining the points (5, 4) and (2. -3) ?

Solution :-

Given points are (5, 4) and (2. -3)

The equation of x -axis is y= 0

Let the point in which divides the linesegment be (x,0)

Let the ratio be m1:m2

Let (x1, y1) = (5,4) => x1 = 5 and y1 = 4

Let (x2, y2) = (2,-3) => x2 = 2 and y2 = -3

We know that

The section formula

({m1x2+m2x1}/(m1+m2) , {m1y2+m2y1}/(m1+m2))

On substituting these values in the above formula

=> ({m1)(2)+(m2)(5)}/(m1+m2),

{(m1)(-3)+(m2)(4)}/(m1+m2) )

=> ( {2m1+5m2}/(m1+m2) , {-3m1+4m2}/(m1+m2) )

Now,

(x,0) = ({2m1+5m2}/(m1+m2) , {-3m1+4m2}/(m1+m2))

On comparing both sides then

x = ({2m1+5m2}/(m1+m2)

and 0 = {-3m1+4m2}/(m1+m2))

=> -3m1+4m2 = 0(m1+m2)

=> -3m1+4m2 = 0

=> -3m1 = -4m2

=> 3m1 = 4m2

=> 3 m1/m2 = 4

=> m1/m2 = 4/3

=> m1:m2 = 4:3

The ratio = 4:3

Answer:-

The ratio in which x - axis divides the given linesegment joining the given points is 4:3

Used formulae:-

→ The equation of x-axis is y = 0

Section formula:-

→ The point which divides the given linesegment joining the points (x1, y1) and (x2, y2) in the ratio m1:m2 is ( {m1x2+m2x1}/(m1+m2) , {m1y2+m2y1}/(m1+m2))