Question

find the rartional number which y axis divides line segment (-3,6) and (12,-3)

Answer 1

★ STRAIGHT LINES ★

Let P (0,y) be the point dividing the line segment joining A(-3,6) and B(12,-3) in ratio k:1

Using section formula ,

x co-ordinate of P = [ k(12) + 1(-3) ] / [k+1]
x co-ordinate of P = (12k-3) / (k+1)

and ,

y co-ordinate of P = [ k(-3) + 1(6) ] / [k+1]
y co-ordinate of P = (6 - 3k) / (k + 1)

Now ,
P lies on Y-axis ,

Therefore , x co-ordinate of P = 0

(12k - 3) / (k + 1) = 0

12k - 3 = 0

k = 1/4

Hence , Y-axis divides the line segment joining A(-3,6) and B(12,-3) in ratio 1:4