Question

find the ratio in which the line segment joining the points A(3,8) and B(-9,3) is divided by y axis

Answer 1

here coordinates of dividing point is
(0,y)

p(x,y) = { mx2 + nx1/m+n , my2 + ny1/m+n}

p(0,y) = { m(-9)+n(3)/m+n , m(3)+n(8)/m+n}

p(0,y) = { -9m+3n/m+n , 3m+8n/m+n }

compare both side

0 = -9m+3n/m+n

0(m+n) = -9m+3n

0 = -9m+3n

9m = 3n

m/n = 3/9

m/n = 1/3

m:n = 1:3

so the ratio is 1:3

Answer 2

therefore we get the ratio 1:3 by the section formula