Question

find the coordinate of a point P on y-axis which divides the line segment joining point (- 2, 3) and (4, 3) in the ratio 1:2.​

Answer 1

Step-by-step explanation:

Given :-

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

To find :-

Find the coordinate of a point P on y-axis which divides the line segment joining point (- 2, 3) and (4, 3) in the ratio 1:2. ?

Solution :-

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

Let (x1, y1) = (-2,3) => x1 = -2 and y1 = 3

Let (x2, y2) = (4,3) => x2 = 4 and y2 = 3

We know that

The equation of y-axis is x = 0

The required point on y-axis = (0,y)

Given ratio = 1:2

Let m1:m2 = 1:2 => m1 = 1 and m2 = 2

We know that

By Section formula

The Coordinates of the point P(x,y) 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) )

On Substituting these values in the above formula then

=> ({(1)(4)+(2)(-2)}/(1+2),{(1)(3)+(2)(3)}/(1+2))

=> ((4-4)/3,(3+6)/3))

=> (0/3,9/3)

=> (0,3)

According to the given problem

The required point = (0,y)

=> (0,3) = (0,y)

=> y = 3

The point = (0,3)

Answer:-

The required point for the given problem is (0,3)

Used formulae:-

Section formula:-

The Coordinates of the point P(x,y) 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) )