Determine the ratio in which the point (-6, a) divides the join of A(-3, 1) and B(-8, 9). Also find the value of a.

Here, given points are A(-3, 1) and B(-8, 9) and let the point dividing the line joining two points be C(-6,a).

Let the ratio be m:n

By section formula,

x = , y =

For point C(-6,a),

-6 = …(1)

And a = …(2)

Solving 1 for finding ratio between m and n,

-6 =

-6 (m + n) = -8m -3n

6m + 6n = 8m + 3n

∴ 2m = 3n

∴ =

∴ m : n = 3 : 2

Now solving for equation 2, where m = 3 and n = 2

a =

a =

∴ a =

∴ a =

∴ value of a is