Refer to the diagrams showing drainage patterns. Identify drainage patterns A and B. Differentiate between the underlying rock structure of drainage patterns A and B respectively.

Count streams per order for each basin.

Basin A:
Order 1: 4 streams
Order 2: 2 streams
Order 3: 1 stream

Basin B:
Order 1: 8 streams
Order 2: 4 streams
Order 3: 2 streams
Order 4: 1 stream

$$\begin{align*} &\text{A: Order 1 = 4, Order 2 = 2, Order 3 = 1} \\ &\text{B: Order 1 = 8, Order 2 = 4, Order 3 = 2, Order 4 = 1} \end{align*}$$ $$\boxed{\text{A: 4, 2, 1 \\ B: 8, 4, 2, 1}}$$

Bifurcation ratio $R_b = \frac{N_u}{N_{u+1}}$, average over orders.

For basin A:
$R_b = \frac{4}{2} = 2$, $\frac{2}{1} = 2$. Average $R_b = 2$.

For basin B:
$R_b = \frac{8}{4} = 2$, $\frac{4}{2} = 2$, $\frac{2}{1} = 2$. Average $R_b = 2$.

$$\boxed{\text{A: 2, B: 2}}$$

Horton's law: Number of streams $N_u$ decreases geometrically with order $u$, $N_u \approx R_b^{k-u}$.

Both basins show constant $R_b = 2$, so number halves each higher order.

Both conform to Horton's law.

\boxed{\text{A: Conforms (R_b=2 constant), B: Conforms (R_b=2 constant)}}

Observe from figure: Higher order streams are visibly longer.

Mean stream length $L_u$ increases geometrically with order, $L_u \approx R_l^{u}$ where $R_l >1$ (length ratio).

Lengths approximately double per order (visually).

Both conform.

$$\boxed{\text{A: Increases geometrically with order, B: Increases geometrically with order}}$$

1.b Drainage density

Drainage density $D_d = \frac{\text{Total stream length } L}{\text{Basin area } A}$.

No scale provided, but visually compare spacing.

Basin A: Streams moderately spaced, medium density.

Basin B: More streams, closer spacing, higher density.

Total (combined or average): Medium to high (qualitative, no numerical values given).

Or if grid/count method intended: Estimate $L$ by segment count, $A$ by enclosure.

But figure lacks scale; typically described as:

A: Medium drainage density
B: High drainage density

$$\boxed{\text{A: medium, B: high}}$$