Pen tool for custom paths in Figma - Cell-by-Cell Formula Trace

Sample Data

Coordinates for a custom Bezier curve path created using the Pen tool in Figma.

Cell	Value
A1	Start Point (X)
B1	Start Point (Y)
A2	100
B2	100
A3	Control Point 1 (X)
B3	Control Point 1 (Y)
A4	150
B4	50
A5	Control Point 2 (X)
B5	Control Point 2 (Y)
A6	200
B6	150
A7	End Point (X)
B7	End Point (Y)
A8	250
B8	100

Formula Trace

Bezier Curve Point Calculation at t=0.5

Step 1: Calculate point on cubic Bezier curve using formula: B(t) = (1-t)^3 * P0 + 3*(1-t)^2 * t * P1 + 3*(1-t)*t^2 * P2 + t^3 * P3

Step 2: Calculate X coordinate: (1-0.5)^3 * 100 + 3*(1-0.5)^2 * 0.5 * 150 + 3*(1-0.5)*0.5^2 * 200 + 0.5^3 * 250

Step 3: Sum X terms: 12.5 + 28.125 + 37.5 + 31.25

Step 4: Calculate Y coordinate: (1-0.5)^3 * 100 + 3*(1-0.5)^2 * 0.5 * 50 + 3*(1-0.5)*0.5^2 * 150 + 0.5^3 * 100

Step 5: Sum Y terms: 12.5 + 9.375 + 28.125 + 12.5

Step 6: Final Bezier curve point at t=0.5 is (109.375, 62.5)

Cell Reference Map

    A      B
1 StartX StartY
2  100    100
3 Ctrl1X Ctrl1Y
4  150     50
5 Ctrl2X Ctrl2Y
6  200    150
7 EndX   EndY
8  250    100

References: P0=(A2,B2), P1=(A4,B4), P2=(A6,B6), P3=(A8,B8)

Shows the four key points used by the Pen tool to create a cubic Bezier curve: start point, two control points, and end point.

Result

    A      B      C
1 StartX StartY  Point at t=0.5
2  100    100    (109.375, 62.5)
3  150     50
4  200    150
5  250    100

The calculated point at t=0.5 on the custom path is shown in column C, representing the midpoint on the curve created by the Pen tool.

Sheet Trace Quiz - 3 Questions

What does the variable t represent in the Bezier curve formula?

A The X coordinate of the control point

B The position along the curve from start (0) to end (1)

C The Y coordinate of the end point

D The thickness of the path

Key Result

Cubic Bezier curve point is calculated by weighted sum of start, two control, and end points using parameter t from 0 to 1.

Practice

1. What does the Pen tool in Figma primarily allow you to do?

easy

A. Draw custom shapes by placing points and curves

B. Automatically generate charts from data

C. Import images into your design

D. Create text layers with different fonts

Solution

1. Step 1: Identify the Pen tool's primary function

   The Pen tool is used to create custom shapes by placing points and curves. Options B, C, and D describe other Figma features unrelated to the Pen tool.

2. Final Answer:

   Draw custom shapes by placing points and curves -> Option A

3. Quick Check:

   Pen tool = Draw shapes [OK]

Hint: Pen tool = points + curves for shapes [OK]

Common Mistakes:

• Confusing Pen tool with text or image tools
• Thinking Pen tool auto-generates charts
• Assuming Pen tool only draws straight lines

2. Which action creates a curved point when using the Pen tool in Figma?

easy

A. Click once on the canvas

B. Right-click on the canvas

C. Click and drag on the canvas

D. Double-click on the canvas

Solution

1. Step 1: Determine how to create curved points with the Pen tool

   Clicking once places a straight point; clicking and dragging creates a curved point. Double-click and right-click do not create curves with the Pen tool.

2. Final Answer:

   Click and drag on the canvas -> Option C

3. Quick Check:

   Click+drag = curve point [OK]

Hint: Drag while clicking to curve points [OK]

Common Mistakes:

• Clicking once expecting a curve
• Using double-click instead of drag
• Right-clicking to create points

3. What will happen if you use the Pen tool to place points at (0,0), (100,0), (100,100), and then close the path back to (0,0)?

medium

A. A square shape will be created

B. A triangle shape will be created

C. An open line will be drawn

D. A circle shape will be created

Solution

1. Step 1: Plot the points to determine the closed shape

   The points form corners at (0,0), (100,0), (100,100), and back to (0,0). This is three points forming a closed triangle shape, not a square.

2. Final Answer:

   A triangle shape will be created -> Option B

3. Quick Check:

   Closed path with three points = triangle [OK]

Hint: Close path with three points = triangle [OK]

Common Mistakes:

• Thinking three points make a square
• Assuming open path creates a shape
• Confusing square with triangle

4. You tried to create a curved path with the Pen tool but the curve looks sharp and not smooth. What is the most likely mistake?

medium

A. You closed the path before adding curves

B. You placed points too far apart

C. You used the wrong color for the path

D. You clicked instead of clicking and dragging to create curve handles

Solution

1. Step 1: Diagnose the cause of sharp curves

   Curves require clicking and dragging to create handles; clicking alone makes sharp corners. Closing path, color choice, or point distance do not affect curve smoothness directly.

2. Final Answer:

   You clicked instead of clicking and dragging to create curve handles -> Option D

3. Quick Check:

   Click vs drag for curves = smoothness [OK]

Hint: Drag to curve, click only = sharp corner [OK]

Common Mistakes:

• Ignoring drag for curves
• Blaming color or path closure
• Thinking point distance affects curve shape

5. You want to create a custom star shape using the Pen tool with smooth curves on each point. Which sequence of actions is best?

hard

A. Click to place each star point, then click and drag to curve each segment, finally close the path

B. Click and drag to place all points, then leave the path open

C. Click to place points and leave the path open for a star shape

D. Use the rectangle tool and then convert it to a star

Solution

1. Step 1: Outline the correct sequence for a smooth curved star

   Click to place each star point, then click and drag to curve each segment smoothly, finally close the path to complete the shape.

2. Final Answer:

   Click to place each star point, then click and drag to curve each segment, finally close the path -> Option A

3. Quick Check:

   Click + drag + close path = smooth star [OK]

Hint: Click points, drag curves, close path for shapes [OK]

Common Mistakes:

• Leaving path open for closed shapes
• Not dragging to create curves
• Using wrong tools for star shape