Coordinate systems (absolute, relative, polar) in AutoCAD - Cell-by-Cell Formula Trace

Sample Data

This table shows a starting point at coordinates (10,5). Then a relative move by (3,4) units is applied. Next, a polar move of length 5 at angle 53.13 degrees is applied. The goal is to calculate the final X and Y coordinates after these moves.

Cell	Value
A1	Point
B1	X
C1	Y
A2	Start
B2	10
C2	5
A3	Move (Relative)
B3	3
C3	4
A4	Move (Polar)
B4	5<53.13°
A5	Result X
B5
A6	Result Y
C6

Formula Trace

FinalX = StartX + RelativeX + PolarX FinalY = StartY + RelativeY + PolarY Where PolarX = Length * COS(Angle), PolarY = Length * SIN(Angle)

Step 1: StartX = 10

Step 2: StartY = 5

Step 3: RelativeX = 3

Step 4: RelativeY = 4

Step 5: Polar length = 5, angle = 53.13°

Step 6: PolarX = 5 * COS(53.13°)

Step 7: PolarY = 5 * SIN(53.13°)

Step 8: FinalX = 10 + 3 + 3

Step 9: FinalY = 5 + 4 + 4

Cell Reference Map

    A       B       C
1 | Point |   X   |   Y   |
2 | Start |  10   |   5   |
3 | Move (Relative) |   3   |   4   |
4 | Move (Polar) | 5<53.13° |       |
5 | Result X |       |       |
6 | Result Y |       |       |

Arrows:
B2 -> FinalX calculation
C2 -> FinalY calculation
B3 -> FinalX calculation
C3 -> FinalY calculation
B4 -> PolarX and PolarY calculation

Cells B2, C2 provide the starting coordinates. B3, C3 provide relative move offsets. B4 provides polar move length and angle. These feed into the final X and Y calculations.

Result

    A       B       C
1 | Point |   X   |   Y   |
2 | Start |  10   |   5   |
3 | Move (Relative) |   3   |   4   |
4 | Move (Polar) | 5<53.13° |       |
5 | Result X |  16   |       |
6 | Result Y |       |  13   |

Final coordinates after relative and polar moves are (16, 13).

The final X coordinate is 16 and final Y coordinate is 13 after applying relative and polar moves to the start point.

Sheet Trace Quiz - 3 Questions

What is the value of PolarX in the calculation?

A 4

B 3

C 5

D 6

Key Result

Final coordinates = Start coordinates + Relative move + Polar move (converted to X,Y)

Practice

1. Which coordinate system in AutoCAD uses a fixed origin point as the reference for all points?

easy

A. Polar coordinates

B. Relative coordinates

C. Absolute coordinates

D. Screen coordinates

Solution

1. Step 1: Understand coordinate systems

   Absolute coordinates always measure from a fixed origin point (0,0).

2. Step 2: Compare with other systems

   Relative coordinates measure from the last point, and polar uses distance and angle from the last point.

3. Final Answer:

   Absolute coordinates -> Option C

4. Quick Check:

   Fixed origin = Absolute coordinates [OK]

Hint: Fixed origin means absolute coordinates [OK]

Common Mistakes:

• Confusing relative with absolute coordinates
• Thinking polar uses fixed origin
• Mixing screen coordinates with AutoCAD coordinate systems

2. Which of the following is the correct way to enter a relative coordinate point 5 units right and 3 units up from the last point in AutoCAD?

easy

A. @5,3

B. 5,3

C. #5,3

D. +5+3

Solution

1. Step 1: Recall relative coordinate syntax

   Relative coordinates start with '@' followed by x,y offsets from last point.

2. Step 2: Identify correct syntax

   @5,3 uses '@5,3' which means 5 units right and 3 units up from last point.

3. Final Answer:

   @5,3 -> Option A

4. Quick Check:

   Relative coordinates start with '@' [OK]

Hint: Relative coordinates always start with '@' [OK]

Common Mistakes:

• Omitting '@' for relative coordinates
• Using commas incorrectly
• Confusing relative with absolute coordinates

3. If the last point entered is at (10, 10), what absolute coordinate point does @5<45 represent in AutoCAD's polar coordinate system?

medium

A. (13.54, 13.54)

B. (15, 15)

C. (5, 45)

D. (10, 10)

Solution

1. Step 1: Understand polar coordinate input

   @5<45 means move 5 units at 45 degrees from last point (10,10).

2. Step 2: Calculate x and y offsets

   x offset = 5 * cos(45°) ≈ 3.54, y offset = 5 * sin(45°) ≈ 3.54.

3. Step 3: Add offsets to last point

   New point = (10 + 3.54, 10 + 3.54) = (13.54, 13.54).

4. Final Answer:

   (13.54, 13.54) -> Option A

5. Quick Check:

   Polar offset + last point = (13.54, 13.54) [OK]

Hint: Use cos/sin for polar offsets, add to last point [OK]

Common Mistakes:

• Using angle in degrees as x or y directly
• Forgetting to add offsets to last point
• Mixing absolute and relative coordinates

4. You entered the point @10,5 in AutoCAD but the point appeared at (10,5) instead of relative to the last point. What is the likely error?

medium

A. You forgot to include '@' before coordinates

B. You typed '@10,5' but the last point was at (0,0)

C. You entered absolute coordinates instead of relative

D. You used polar coordinates syntax incorrectly

Solution

1. Step 1: Analyze the entered point and result

   Entered @10,5 means relative 10 right, 5 up from last point.

2. Step 2: Check last point position

   If last point was (0,0), relative point is (10,5), matching the result.

3. Step 3: Identify cause of confusion

   User expected relative to a different last point, but last point was origin.

4. Final Answer:

   You typed '@10,5' but the last point was at (0,0) -> Option B

5. Quick Check:

   Relative point depends on last point [OK]

Hint: Check last point before entering relative coordinates [OK]

Common Mistakes:

• Assuming '@' was missing when it was present
• Confusing absolute and relative inputs
• Ignoring last point position

5. You want to draw a line starting at absolute point (20, 30). Then draw a second line 10 units away at 60 degrees from the first point using polar coordinates. What is the correct coordinate input for the second point?

hard

A. 20,30

B. 10<60

C. @20,30

D. @10<60

Solution

1. Step 1: Start at absolute point (20,30)

   Enter 20,30 to set the first point absolutely.

2. Step 2: Use polar relative coordinate for second point

   To move 10 units at 60 degrees from last point, use @10<60.

3. Step 3: Confirm coordinate input

   @10<60 correctly uses '@' for relative and '<' for angle in polar format.

4. Final Answer:

   @10<60 -> Option D

5. Quick Check:

   Polar relative input = '@distance<angle' [OK]

Hint: Use '@distance

Common Mistakes:

• Omitting '@' for relative polar coordinates
• Using absolute coordinates for second point
• Confusing angle symbol '<' with comma