30. a) Find the co-ordinates of the points of trisection of the line segment joining $$ (-3,-5) $$ and $$ (-6,-8) $$

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We are given the points 
$$
A=(-3,-5) \quad \text{and} \quad B=(-6,-8)
$$
and we need to find the points which trisect the line segment joining $$ A $$ to $$ B $$.

Let the points of trisection be $$ P $$ (closer to $$ A $$) and $$ Q $$ (closer to $$ B $$). This means that the segment is divided into three equal parts. Thus, the ratios are:
- $$ AP:PB = 1:2 $$ for $$ P $$
- $$ AQ:QB = 2:1 $$ for $$ Q $$

We will use the section formula for internal division. If a point $$ R $$ divides the line joining $$ (x_1, y_1) $$ and $$ (x_2, y_2) $$ in the ratio $$ m:n $$, then
$$
R = \left(\frac{n x_1 + m x_2}{m+n}, \frac{n y_1 + m y_2}{m+n}\right).
$$

### Finding Point $$ P $$ (Ratio $$ 1:2 $$)
Here, $$ P $$ divides $$ AB $$ in the ratio $$ 1:2 $$ (i.e. $$ AP:PB = 1:2 $$). Thus, we assign:
$$
m=1 \quad \text{(portion towards $$ B $$)}, \quad n=2 \quad \text{(portion towards $$ A $$)}.
$$

Substitute into the formula:
$$
P = \left(\frac{2(-3) + 1(-6)}{1+2}, \frac{2(-5) + 1(-8)}{1+2}\right).
$$

Calculate the coordinates:
$$
x_P = \frac{-6 - 6}{3} = \frac{-12}{3} = -4,
$$
$$
y_P = \frac{-10 - 8}{3} = \frac{-18}{3} = -6.
$$

Thus, 
$$
P=(-4,-6).
$$

### Finding Point $$ Q $$ (Ratio $$ 2:1 $$)
Next, $$ Q $$ divides $$ AB $$ in the ratio $$ 2:1 $$ (i.e. $$ AQ:QB = 2:1 $$). Here, we assign:
$$
m=2 \quad \text{(portion towards $$ B $$)}, \quad n=1 \quad \text{(portion towards $$ A $$)}.
$$

Substitute into the section formula:
$$
Q = \left(\frac{1(-3) + 2(-6)}{2+1}, \frac{1(-5) + 2(-8)}{2+1}\right).
$$

Calculate the coordinates:
$$
x_Q = \frac{-3 - 12}{3} = \frac{-15}{3} = -5,
$$
$$
y_Q = \frac{-5 - 16}{3} = \frac{-21}{3} = -7.
$$

Thus, 
$$
Q=(-5,-7).
$$

### Final Answer
The coordinates of the points of trisection of the line segment are:
$$
\boxed{(-4,-6) \quad \text{and} \quad (-5,-7)}.
$$
The points that trisect the line segment joining $$ (-3,-5) $$ and $$ (-6,-8) $$ are $$ (-4,-6) $$ and $$ (-5,-7) $$.

a) Find the co-ordinates of the points of trisection of the line segment joining and

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