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

Answer 1

(-4,-6) =(x1,y1), (10,12) = (x2,y2)
let the(0,y) on y-axis divides the joining of above points in the ratio k:1
using section formula
[(k*10+1*(-4))/(K+1) , (k*12+1*(-6))/(k+1)] = (0,y)


equating x- co ordinates
(10k-4)/(k+1) =0

10k-4 = 0
10k=4
k=4/10
k=2/5-----(1)
therefore
ratio = 2:5
equating y co ordinates
(12k-6)/(k+1) = y

(12*2/5 -6)/(2/5+1) =y
[(24-30)/5]/(2+5)/5 =y
-6/7 = y
required point = (0,y) = (0,-6/7)