Slope and Gradient Calculation

During a mapwork exercise on a topographical map with a scale of $1 : 100,000$, a student identifies a river bed at an elevation of $120\text{ m}$ and a hilltop trigonometric station at an elevation of $320\text{ m}$. If the map distance between these two points is $4\text{ cm}$, what is the average gradient of the slope?

Match each topographic map elevation scenario to its corresponding calculated slope gradient ratio ($1 \text{ in } N$). Which of the following correct pairs match each map measurement scenario on the left with its computed gradient ratio on the right?

A proposed road route on a topographical map drawn to a scale of $1 : 20,000$ connects a river confluence at an elevation of $140\text{ m}$ to a hilltop beacon at an elevation of $340\text{ m}$. If the distance measured along the route on the map is $8\text{ cm}$, what is the average gradient of the slope along this route?

Match each set of elevation and ground distance measurements to its corresponding slope gradient ratio.

On a topographical map, Point X is situated at an elevation of $200\text{ m}$ and Point Y is situated at an elevation of $500\text{ m}$. If the horizontal ground distance between the two points is $6\text{ km}$, what is the gradient of the slope from Point X to Point Y expressed as a ratio?

A topographic map with an original scale of $1 : 50,000$ is reduced to half its linear size. On the reduced map, the measured distance between Point X (elevation $750\text{ m}$) and Point Y along a slope is $5.0\text{ cm}$. If Point Y lies $8$ contour intervals below Point X on a map with a contour interval of $25\text{ m}$, what is the gradient between Point X and Point Y expressed as a ratio?

On a topographical map drawn to a scale of $1 : 50,000$, Point X is situated at an elevation of $150\text{ m}$ and Point Y is situated at an elevation of $400\text{ m}$. If the straight-line distance between Point X and Point Y measured on the map is $5\text{ cm}$, what is the slope gradient between the two points expressed as a percentage?

On a topographical map drawn to a scale of $1 : 25,000$, two hilltop stations, Station A and Station B, are separated by a map distance of $16\text{ cm}$. If Station A is situated at an elevation of $580\text{ m}$ above sea level and Station B is at an elevation of $180\text{ m}$, what is the gradient of the slope between the two stations expressed as the value $N$ in the ratio $1 : N$?

Match each set of topographic relief measurements to its corresponding slope gradient ratio ($1 \text{ in } N$).

Match each topographic relief profile scenario to its corresponding calculated slope gradient expressed both as a ratio ($1 \text{ in } N$) and as a percentage gradient.

On a topographical map with a scale of $1 : 50,000$, Point X lies on a hilltop at an elevation of $420\text{ m}$, while Point Y sits near a stream bed at an elevation of $170\text{ m}$. If the measured distance between Point X and Point Y on the map is $12.5\text{ cm}$, calculate the slope gradient between the two points. Express your answer as the value of $N$ in the standard gradient ratio $1 : N$ (or $1 \text{ in } N$). What is the value of $N$?

Four survey transects were evaluated on a topographical map drawn to a scale of $1 : 50,000$. Match each transect scenario on the left with its corresponding calculated slope gradient ratio on the right.

On a topographical map drawn to a scale of $1 : 25,000$, Point P is situated at a trigonometric station with an elevation of $520\text{ m}$, while Point Q lies at a stream confluence at an elevation of $370\text{ m}$. The measured straight-line distance between Point P and Point Q on the map is $15\text{ cm}$. What is the slope gradient between Point P and Point Q, expressed as the denominator $N$ in the ratio $1 \text{ in } N$?

Match each topographic map slope calculation scenario on the left with its corresponding calculated gradient representation on the right.

On a topographical map drawn to a scale of $1 : 40,000$, a communications cable line is planned between Trigonometrical Station $P$ at an elevation of $680\text{ m}$ and Spot Height $Q$ at an elevation of $200\text{ m}$. If the straight-line distance measured between $P$ and $Q$ on the map is $12\text{ cm}$, what is the average gradient of the slope between these two points expressed as a percentage?

On a topographical map with a scale of $1 : 20,000$, a proposed electric transmission line extends from Point $K$ situated on a ridge contour of $650\text{ m}$ to Point $L$ located near a stream contour of $450\text{ m}$. If the measured distance between Point $K$ and Point $L$ on the map is $8.0\text{ cm}$, what is the gradient of the slope between these two points?

Match each slope measurement scenario on the left with its corresponding calculated gradient on the right.

A topographical map extract drawn to a scale of $1 : 100,000$ shows a footbridge over a stream at an elevation of $250\text{ m}$ and a forest observation tower situated on a hilltop at an elevation contour of $450\text{ m}$. If the straight-line distance between the bridge and the tower measured on the map is $4\text{ cm}$, what is the average gradient of the slope between these two locations?