# VectorPaint triangle medians: check midpoints and the two-thirds centroid position

Language: en
Canonical: [VectorPaint triangle medians: check midpoints and the two-thirds centroid position](<https://allluckly.cn/en/guides/vectorpaint-triangle-median-centroid/>)
中文：[中文 HTML](<https://allluckly.cn/guides/vectorpaint-triangle-median-centroid/>)
English: [English HTML](<https://allluckly.cn/en/guides/vectorpaint-triangle-median-centroid/>)
Published: 2026-11-07T00:00:00+08:00
Modified: 2026-11-07T09:41:37+08:00
Author: Bison

Calculate side midpoints and centroid from three vertices, then draw medians without confusing different triangle centres.

English translation of the [Chinese original](<https://allluckly.cn/guides/vectorpaint-triangle-median-centroid/>), translated on 2026-11-07. Original publication dates, attribution, code and version notes are retained.

A triangle centroid is not an eyeballed central point: each median joins a vertex to its opposite side midpoint. Use invented coordinates to draw triangle, medians and centroid and check concurrence. Objects are not automatically constrained, and a plausible intersection is no certified geometry or measured physical centre of mass.

## Fix three vertices and coordinate orientation

Create a 1000 by 800 pixel canvas with x rightward/y downward and A=(200,600), B=(800,600), C=(500,150). Record coordinates externally before closing three edges. These are screen, not geographic/physical coordinates. AB is the lower horizontal base with C above; verify y orientation. Keep labels clear of points and selections explicit. Save original vertices/edges so moving any vertex prompts the correct edge/median updates.

## Average endpoints for each side midpoint

Midpoints are AB=(500,600), BC=(650,375), CA=(350,375), averaging x/y separately. Verify rather than assuming a selection-box centre supplies the answer. Give each midpoint a distinct side identity. It lies within its side with equal endpoint distances; manual placement is referential, not decimal measurement certification. Two midpoint heights coincide because this example is symmetric, not as a universal triangle property.

## Join vertices only to opposite midpoints

Join A→midpoint BC, B→midpoint CA and C→midpoint AB. A line to an adjacent midpoint is not the required median. Inspect endpoint ownership in temporary colours, then restore one style. Medians differ from angle/perpendicular bisectors even where symmetry makes some coincide. Hide the centroid marker and inspect concurrence before calculations rather than placing a point and bending lines toward it.

## Average all three vertices for the centroid

Compute x=(200+800+500)/3=500 and y=(600+600+150)/3=450. Check arithmetic separately from point placement; do not mix vertices and midpoints in another average. G=(500,450) lies inside and on all medians. Its lower appearance is appropriate: distances to top vertex and base midpoint differ. Do not move it to half the height for visual centring. This mathematical centroid does not establish the mass centre of nonuniform material.

## Check the two-to-one division on one median

C→midpoint AB is 450 pixels vertically; C→G is 300 and G→midpoint 150, ratio 2:1. G is two-thirds from the vertex, not an ambiguously measured two-thirds from the midpoint. Check other medians through coordinate displacement without using vertical difference as slanted length. This explains known coordinates, not measured line lengths from dragging. Keep any dimension arrows clear of endpoints and establish orientation before ratio labels.

## Update dependencies after moving the top vertex

Move C to (500,300) in a copy with A/B fixed. New G=(500,500); midpoint AB remains (500,600), while BC/CA become (650,450)/(350,450). Recalculate before moving and reconnect all edges/medians, not just C. The vertical median is now 300 with 200/100 portions, still 2:1. Save versions separately at equal size; ordinary paths do not preserve these dependencies automatically.

## Inspect vertices, midpoints and centroid in output

Retain coordinates, edges, medians and markers. In export, check vertices before midpoints/G. Reduce crowded median weights without separating the shared intersection. Test backgrounds; backing objects remain. Name median-centroid teaching diagram, coordinate revision and size and exclude moved-C tests. Explain independent point/line maintenance in editable delivery rather than claiming automatic geometric constraints from a format. Physical/engineering measurement needs separate validation; this checks drawing-coordinate relationships.

## Check opposite sides and averages for nonconcurrent medians

For nonconcurrence, check opposite-side ownership then midpoint averages. A central-looking wrong point needs the vertex average, not bent lines. Resolve reversed ratios through vertex/midpoint orientation. A changed base midpoint after moving C suggests accidental selection. Recheck vertices, midpoints, medians and ratios so each point has a derivation rather than an arbitrary intersection with a mathematical label.

## Related tutorials and sources

[VectorPaint grids and guides: composition references for icons and posters](<https://allluckly.cn/en/guides/vectorpaint-grid-guides/>), [VectorPaint three-step paired views: map plan treads to side-view heights](<https://allluckly.cn/en/guides/vectorpaint-three-step-two-view/>).

Sources checked on November 7, 2026: VectorPaint 1.0.8, requiring iOS / iPadOS 17.0 or later. Capability scope follows the [official App Store description](<https://apps.apple.com/cn/app/id1587272880>) and [Apple public version lookup](<https://itunes.apple.com/lookup?id=1587272880&country=cn>). These are exercises and checks you can perform, without a claim of step-by-step physical-device testing or verification in every target environment. Example content is instructional; follow the controls in your installed version.