---
title: "Consecutive, independent coordinates, plotting"
subject: "Surveying II"
chapter: 1
key: "semester_4/surveying_ii:consecutive-independent-coordinates-plotting"
source: https://www.bctengineer.com/q/semester_4/surveying_ii/consecutive-independent-coordinates-plotting
site: BCT Engineering
---

# Consecutive, independent coordinates, plotting

Surveying II · Chapter 1: Traversing

- Asked in: 2072 Magh, 3+3 marks
- Video: [dependent & independent co-ordinate surveying ||total & consecutive co-ordinate surveying #traverse](https://www.youtube.com/watch?v=8YK58E5vP1Q) — Aim 2 Civil Class
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/surveying_ii/consecutive-independent-coordinates-plotting
- Whole chapter: https://www.bctengineer.com/md/semester_4/surveying_ii/chapter-1

## Question

Describe consecutive and independent coordinates. Explain the plotting method of traverse by grid coordinates.

## Short answer

Consecutive coordinates are latitude and departure from the previous station. Independent coordinates are total northing and easting from a common origin. Plotting by grid coordinates uses a drawn grid; station positions are plotted from independent coordinates using a scale, then joined and checked. Errors do not accumulate.

## Answer

#### Consecutive and independent coordinates
**Consecutive (dependent) coordinates:** the latitude and departure of a line, i.e. the coordinates of its end point measured from the preceding station taken as origin. Example: line AB with $L=100$ m and bearing $60^\circ$ gives $\Delta N=100\cos 60^\circ=+50$ m and $\Delta E=100\sin 60^\circ=+86.6$ m from A.

**Independent (total) coordinates:** the northing and easting of a station measured from one common origin (the reference station or a national grid). They are the algebraic sum of the consecutive coordinates from the origin. Example: if A is $(1000,\,1000)$, then B is $(1050,\,1086.6)$, and C is B plus the consecutive coordinates of BC.

Independent coordinates are used for plotting because all stations refer to one origin, so plotting errors do not accumulate.

#### Plotting a traverse by grid coordinates
1. Choose a scale so that the whole traverse fits on the sheet (for example 1 cm = 10 m). Find the range of N and E, subtract the minimum values and divide by the scale to get the size needed.
2. Draw the grid of squares (the grid sheet) and label the grid lines with the independent northing (vertical axis) and easting (horizontal axis) values, choosing an origin near the south-west corner so that all coordinates are positive.
3. Convert each station's independent coordinates to plotting units. For example, with scale 1 cm = 10 m, a station at $(N, E)$ is at $(E-E_0)/10$ cm along the east axis and $(N-N_0)/10$ cm along the north axis from the origin.
4. Mark each station with a fine pencil dot by measuring its coordinates from the nearest grid lines with a scale (no protractor is needed), and circle it and write the station name.
5. Join the stations in order with thin lines and check that each plotted line length, measured with the scale, agrees with the field length. This is a check for blunders.
6. Plot details (offsets and radiations) from the stations, ink the map and add the title, scale, north arrow, legend and border.

Advantage: each station is located independently from its coordinates, so plotting errors do not accumulate and the plotted traverse closes exactly.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What are consecutive (dependent) coordinates of a line?
   A. The northing and easting of a station from the common origin
   B. The latitude and departure of the line, measured from the preceding station
   C. The sum of all latitudes in the traverse
   D. The coordinates read from a map grid
   Answer: B. Consecutive coordinates are the latitude and departure of a line, taking the previous station as origin. (Key point: Consecutive coordinates)

2. Why are independent coordinates used for plotting a traverse?
   A. They are shorter numbers
   B. All stations refer to one origin, so plotting errors do not accumulate
   C. They avoid the need for a scale
   D. They remove the need for field angles
   Answer: B. Each station is plotted directly from the same origin, so an error in one station does not carry into the next. (Key point: Why independent coordinates for plotting)

3. After plotting stations from grid coordinates, how is blunder checked?
   A. Measure each plotted line with the scale and compare with the field length
   B. Redraw the grid at a different scale
   C. Check the colour of the pencil dots
   D. Measure only the grid squares
   Answer: A. The scaled length of each plotted line should agree with the field length, otherwise a blunder exists. (Key point: Plotting check)

## Related in Surveying II

- [Closed/open traverse, consecutive, independent coordinates](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Aclosed-open-traverse-consecutive-independent) — Surveying II, chapter 1
- [Closed loop/link traverse, grid plotting](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Aclosed-loop-link-traverse-plotting-grid) — Surveying II, chapter 1
- [Plotting coordinated traverse on grid paper](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Atraverse-plotting-grid-paper) — Surveying II, chapter 1, asked 2×
- [Balancing traverse, methods, independent coordinates](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Abalancing-traverse-methods-independent-coordinates) — Surveying II, chapter 1
- [Omitted measurement cases, traverse plotting](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Aomitted-measurement-cases-plotting) — Surveying II, chapter 1
- [Link traverse B to M, coordinates X and Y](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Alink-traverse-bowditch-x-y-between) — Surveying II, chapter 1

## Related in other subjects

- [Closing error; plotting methods in compass traverse](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Aclosing-error-plotting-methods) — Surveying I, chapter 4
- [Plotting theodolite traverse; repetition errors](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Aplotting-theodolite-traverse-repetition-errors) — Surveying I, chapter 7
- [Area of traverse by DMD and coordinates (N/S/E/W)](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Aarea-closed-traverse-nswe-108) — Surveying I, chapter 9