Question

1. the line segment on the map below is 1.6 cm long, and the map scale is 1 cm = 0.5 km. what is the gradient of the slope marked by the line

Explanation:

Step1: Calculate the actual - distance

Given the map - scale 1 cm = 0.5 km and the map length of the line segment is 1.6 cm. The actual distance $d$ is calculated by multiplying the map length by the scale factor.
$d = 1.6\times0.5=0.8$ km. Since 1 km = 1000 m, $d = 0.8\times1000 = 800$ m.

Step2: Determine the gradient

The gradient of a slope is the ratio of the vertical change to the horizontal change. But since no vertical - change information is given in the problem description and we assume the problem is asking for the scale in terms of length ratio. The scale can be written as a ratio of map distance to actual distance.
The map distance is 1.6 cm and the actual distance is 800 m or 80000 cm. The ratio is $\frac{1.6}{80000}=\frac{1}{50000}$. In terms of m/km, 1 cm on the map represents 0.5 km in reality. So the scale is 500 m/km.

Answer:

500 m/km