Regarding the design of a basic voltage divider
In general, voltage division applies to the voltage across a resistor in series with one or more other resistors.

For example, assume that we have \$N\$ series connected resistors and, further, that the voltage across the series combination is \$V_S\$.

Then, the voltage across the \$n^{th}\$ resistor is given by the general voltage division formula:

$$V_{R_n} = V_S \frac{R_n}{R_1 + R_2 +\; ... \; + R_{N-1} + R_N} =  $$

In the diagram you provide, it happens to be the case that 

$$V_{out} = V_{R_2}$$

And, by the general voltage division formula applied to two series connected resistors

$$V_{R_2} = V_{in} \frac{R_2}{R_1 + R_2}$$

Thus,

$$V_{out} = V_{in} \frac{R_2}{R_1 + R_2}$$

Note that we could have chosen \$V_{out}\$ to be the voltage across \$R_1\$ instead though this isn't often the case.

In most cases, the output voltage is referenced to ground and, so, the output voltage is taken across the resistor with one terminal grounded.

In summary, voltage division is more general than the two resistor voltage divider circuit you've provided.  The principle of voltage division and the general formula is a valuable 'tool' in one's circuit solving 'toolkit'.