Question

The line segment joining the points (3, 5) and (-4, 2) is divided by y- axis in the ratio
5:3
3:5
4:3
3:4​

Answer 1

Answer:

Correct option is

D

3:4

Using the section formula, if a point (x,y) divides the line joining the points (x1,y1) and (x2,y2) in the ratio m:n, then (x,y)=(m+nmx2+nx1,m+nmy2+ny1)

Substituting (x1,y1)=(3,5) and (x2,y2)=(−4,2)  in the section formula, we get the point 

(m+nm(−4)+n(3),m+nm(2)+n(5))

Since the point of intersection lies on the y-axis, x-coordinate =0 

m+n−4m+3n=0 

⇒−4m+3n=0

⇒4m=3n 

⇒m:n=3:4

Answer 2

Given: Two points (3,5) and (-4,2) is divided by the y axis

To find: The ratio of division

Explanation: Let the y axis divide the two points in the ratio k:1.

The formula for finding point of division in case of internal division is:

(x,y)= m*x2 + n*x1 / m+n, m*y2 + n*y1/ m+n

Here, m= k, n=1 ,x1 = 3, y1=5 , x2 = -4 and y2= 2

Using the values in the above formula the point of division can be written as:

(x,y) = k * -4 + 1 *3/ k+1 , k* 2 + 1* 5/ k+1

= -4k+3/ k+1 , 2k+5/ k+1

Since y axis divides these points and x coordinates of any point on y axis is 0, therefore, the x coordinates of the point of division is also 0.

Therefore,

-4k+3/ k+1 = 0

=> -4k+3 = 0

=> -4k = -3

=> 4k = 3

=> k = 3/4

Therefore, the y axis divides these points in the ratio of option (d) 3:4.