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

Let given points be A (-3, -1) and B (-8, -9).

Let the point C(-5, -21 /5) divide AB in ratio m:n.

By section formula,

x = , y =

For point C(-5, -21 /5) on the line joined by the points A and B.

-5 = …(1)

And, - = …(2)

Solving 1,

-5(m + n) = -8m - 3n

∴5m + 5n = 8m + 3n

∴ 2n = 3m

∴ =

Hence, ratio is 2:3.