Answer
(a) The average rate of change from $A$ to $B$ is zero.
(b) The average rate of change from $A$ to $C$ is
$\frac{{\Delta altitude}}{{\Delta horizontal}} = \frac{{ - 6}}{{\sqrt {17} }}$
Work Step by Step
(a) From $A$ to $B$, there is no change in altitude. Therefore, average rate of change is zero.
(b) From Figure 25 we see that the contour interval is $m=3$. From $A$ to $C$ it spans two level curves, so the change in altitude is $\Delta altitude = - 6$.
From $A$ to $C$, the horizontal change is the distance $\overline {AC} $
$\Delta horizontal = \sqrt {{{\left( {6 - 2} \right)}^2} + {{\left( {5 - 4} \right)}^2}} = \sqrt {17} $
So, the average rate of change from $A$ to $C$ is
$\frac{{\Delta altitude}}{{\Delta horizontal}} = \frac{{ - 6}}{{\sqrt {17} }}$
