Question

Calculate the ratio in which the line segment joining (3, 4) and (-2, 1) is divided by the y-axis. (ICSE 1991)​

Answer 1

Step-by-step explanation:

Given :-

The points are (3, 4) and (-2, 1)

To find :-

Calculate the ratio in which the line segment joining (3, 4) and (-2, 1) is divided by the y-axis.?

Solution :-

Given points are (3, 4) and (-2, 1)

We know that

The equation of y-axis is x = 0

Let the point be (0,y)

Let the ratio in which the linesegment joining the points is divided by the y-axis be m1:m2

We know that

The coordinates of the point which divides the linesegment joining the points (x1, y1) and (x2, y2) in the ratio m1:m2 is

( (m1x2-m2x1)/(m1+m2),

(m1y2+m2y1)/(m1+m2) )

According to the given problem

=> (0,y) = ( {(m1)(-2)+(m2)(3)}/(m1+m2) ,

{(m1)(1)+(m2)(4)}/)m1+m2) )

=>(0,y)=({-2m1+3m2}/(m1+m2),

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

On comparing both sides then

(-2m1+3m2)/(m1+m2) = 0 and

(m1+4m2)/(m1+m2)=y

=> -2m1+3m2 = 0(m1+m2)

=> -2m1+3m2 = 0

=> -2m1 = -3m2

=> 2m1 = 3m2

=> m1/m2 = 3/2

=> m1 : m2 = 3:2

Answer:-

The required ratio for the given problem is 3:2

Used formulae:-

Section formula:-

The coordinates of the point which divides the linesegment joining the points (x1, y1) and (x2, y2) in the ratio m1:m2 is

((m1x2-m2x1)/(m1+m2),

(m1y2+m2y1)/(m1+m2))