Question

find the ratio in which the y-Axis divides the line segment joining the points (- 4, - 6) and (10,12). also find the coordinates of the point of division.
plz help me

Answer 1

let the coordinates of the point be (0,y) and y-axis divides the line segment in the ratio k :1.

(0,y) = {(10k-4)/k+1 ,(12k-6)/k+1}

0=10k-4/k+1

10k =4

k=2/5 ==>the ratio of division is 2:5

now, y =(12k-6)/k+1

y={(12*2/5) -6}/(2/5)+1

y =-6/7

thus the coordinates of the point is (0,-6/7)

hope it helps...

Answer 2

let the point in the y axis dividing them be P and its coordinates be(0,y)

let the ratio dividing the segment be k:1

Therefore, by section formula

0=10k+(-4)/k+1

0=10k-4

4=10k

4/10=k

2/5=k

thus, the ratio is 2/5:1

                          =2:5

Now by section formula

y=my₂+ny₁/m+n

y =2*12+5*(-6)/2+5

y=24-30/7

y=-6/7