Question

(i) In what ratio is the line segment joining the points (-2, -3) and (3, 7) divided by the yaxis? Also, find the coordinates of the point of division. 

(ii) In what ratio is the line segment joining (-3, -1) and (-8, -9) divided at the point (−5,−21/5)?

Answer 1

Suppose y - axis divides PQ in the ratio K:1 at R 

Then, the coordinates of the point of division are:

Since, R lies on y - axis and x - coordinate of every point on y - axis is zero

Hence, the required ratio is 2/3:1

i.e., 2:3

Putting K=2/3 in the coordinates of R

We get, (0,1)

Let the point P divide AB in the ratio K:1

Then, the coordinates of P are

But the coordinates of P are given as (−5,−21/5)

Hence, the point P divides AB in the ratio 2/3:1 => 2:3