Question

Find the ratio in which the y-axis divides the line segment joining the points A(-4,2) and B(3,9). Also find the coordinates of the point of division.​

Answer 1

Answer:

Step-by-step explanation:

Let us consider the ratio as k:1 and the point in y-axis which divides the line as (0,y) [ x-coordinate is zero because the point is in y-axis].

=>  $P(x,y)=( \frac{mx_{2}+nx_{1}}{m+n} ,\frac{my_{2}+ny_{1}}{m+n} )$

=> $P(0,y)=(\frac{3k-4}{k+1} ,\frac{9k+2}{k+1} )$

On comparing the x-coordinates,

=> $0=\frac{3k-4}{k+1}$

=> 3k - 4 = 0

Therefore k =  $\frac{3}{4}$

=> k:1 =  $\frac{3}{4}:1$

Hence the ratio is 3:4

On comparing y-coordinates

=> $y=\frac{9(\frac{3}{4})+2 }{\frac{3}{4}+1 }$

=> y = $\frac{\frac{27+8}{4} }{\frac{3+4}{4} }$

=> 7y = 35

=>  y = 5

The coordinate is (0,5)