Question

He ratio in which the y- axis divides the line segment joining the points a(-15,5) and b(9,20) is

Answer 1

The ratio in which the y- axis divides the line segment joining the points a(-15,5) and b(9,20) is 5 : 3

Explanation:

Given:

Coordinates of point A and B respectively are (-15, 5) and (9, 20)

To find out:

The ratio in which the y-axis divides the line segment joining A and B

Solution:

We know that if a point $P(x,y)$ divides the line segment joining two points $A(x_1,y_1)$ and $B(x_2,y_2)$ internally in the ratio $m:n$

Then

$x=\frac{mx_2+nx_1}{m+n}$

$y=\frac{my_2+ny_1}{m+n}$

Coordinate of any point on y axis will be $(0,y)$

Thus,

$0=\frac{m\times 9+n\times (-15)}{m+n}$

$\implies 9m-15n=0$

$\implies 9m=15n$

$\implies \frac{m}{n}=\frac{15}{9}$

$\implies \frac{m}{n}=\frac{5}{3}$

$\implies m:n=5:3$

Hope this answer is helpful.

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