Question

Find the ratio in which the point C divides segment AB, if `5bara + 4barb - 9barc = bar0`

Answer 1

Let `5bara + 4barb - 9barc = bar0`

∴ `9barc = 5bara + 4barb`

∴ `barc = (5bara + 4barb)/9`

= `(5bara + 4barb)/(5 + 4)`

= `(4barb + 5bara)/(4 + 5)`

This is of the form

`(mbarb + nbara)/(m + n)` in which the ratio is m : n

∴ The ratio is 4 : 5

∴ C divide AB internally in the ratio 4 : 5