Solve equilateral triangle coordinates using flexible geometry inputs. View vertices, centroid, area, and perimeter fast. Save practical outputs for lessons, checks, reports, and worksheets.
| Example | Input | Output Highlight |
|---|---|---|
| Two vertices | A(0, 0), B(4, 0) | C can be (2, 3.464102) or (2, -3.464102) |
| Angle method | A(1, 1), side 6, angle 30°, CCW | B and C are rotated from the start vertex |
| Centroid check | Any valid equilateral triangle | Centroid equals the average of all three vertices |
Distance between two known vertices: s = √((Bx - Ax)² + (By - Ay)²)
Midpoint of AB: M = ((Ax + Bx) / 2, (Ay + By) / 2)
Altitude: h = (√3 / 2) × s
Third vertex from two points: C = M ± h × (-dy / s, dx / s)
Second vertex from angle: B = A + s × (cos θ, sin θ)
Third vertex from angle: C = A + s × (cos(θ ± 60°), sin(θ ± 60°))
Centroid: G = ((Ax + Bx + Cx) / 3, (Ay + By + Cy) / 3)
Area: (√3 / 4) × s²
Perimeter: 3 × s
Equilateral triangle coordinate work is common in school and design. A calculator removes repeated plotting errors. It also speeds up coordinate geometry tasks. Every side in an equilateral triangle has the same length. Every interior angle is sixty degrees. That symmetry makes coordinate solving reliable. This page helps you compute missing vertices, centroid values, perimeter, area, and altitude from practical geometry inputs.
You can solve the triangle in two useful ways. The first method starts with two known vertices. When points A and B are known, the calculator finds the two valid third vertices. One sits to the left of segment AB. The other sits to the right. The second method starts with one vertex, side length, and a direction angle. The page then builds the remaining coordinates from rotation rules. This makes the tool useful for graphing, drafting, and coordinate verification.
The result block shows the coordinates clearly above the form. That layout improves review and comparison. Students can check homework faster. Teachers can build examples quickly. Engineers can verify triangular layouts before plotting larger models. Developers can also use the outputs for graphics, games, and geometric transformations. Because the calculator returns centroid coordinates, it also supports balance point analysis. The area, perimeter, and altitude values provide fast geometric summaries for reports and worksheets.
Accuracy matters in coordinate geometry. Enter values with consistent units. Use decimal precision when needed. If you choose the two vertex method, remember that two mirror solutions exist. If you choose the angle method, select the correct orientation. Counterclockwise and clockwise give different third vertices. After calculation, export the results to CSV for spreadsheets or to PDF for printable notes. The example table, formulas, and FAQ section below help you understand each output and apply it correctly in classwork, assessments, and real coordinate geometry practice. This calculator is also useful for visual reasoning. Symmetric coordinates make pattern checks easier. You can compare vertex spacing, inspect centroid placement, and confirm equal side construction without manual trigonometric repetition. That reduces mistakes in exams and project drafts. With one page, you get calculation, reference content, export tools, and worked examples in a simple coordinate workflow for everyday use.
It finds equilateral triangle coordinates from either two known vertices or from one vertex with side length and direction angle. It also returns centroid, area, perimeter, and altitude.
A fixed segment AB can support an equilateral triangle on either side of the line. That creates one left solution and one right solution.
The centroid is the average position of the three vertices. It is often called the triangle balance point and is useful in geometry and graphics work.
Yes. The calculator accepts positive, negative, and decimal coordinates. That makes it useful for all quadrants of the Cartesian plane.
No. Any numeric angle works. Standard trigonometric rotation handles values above 360 degrees or below 0 degrees correctly.
Use any consistent linear unit for coordinates and side length. The calculator does not convert units, so keep all inputs in the same system.
The PDF export creates a simple printable record of the current result. It is helpful for notes, worksheets, reviews, and documentation.
Use the angle method when you know one starting vertex, the side length, and the direction of one side. It is helpful for plotting and drafting.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.