3rd Vertex Triangle Calculator

Finds third vertex given conditions:

\[ x_3 = ..., \text{ solve from equations} \]

Vertex 1 X-coordinate:

Vertex 1 Y-coordinate:

Vertex 2 X-coordinate:

Vertex 2 Y-coordinate:

Condition:

Possible Third Vertex Coordinates:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the 3rd Vertex Triangle Calculator?

This calculator determines the possible coordinates of the third vertex of a triangle when given two vertices and a specific condition (equilateral triangle or right angle at the third vertex).

2. How Does the Calculator Work?

The calculator uses geometric principles to solve for the third vertex:

For equilateral triangle: \[ \text{Height} = \frac{\sqrt{3}}{2} \times \text{Side length} \] For right angle: \[ (x_3-x_1)(x_3-x_2) + (y_3-y_1)(y_3-y_2) = 0 \]

Where:

\( (x_1, y_1) \) — First vertex coordinates
\( (x_2, y_2) \) — Second vertex coordinates
\( (x_3, y_3) \) — Third vertex coordinates to find

Explanation: The calculator uses vector mathematics and geometric properties to determine possible positions of the third vertex.

3. Importance of Triangle Vertex Calculation

Details: Finding the third vertex is important in computer graphics, CAD design, navigation systems, and geometric problem solving.

4. Using the Calculator

Tips: Enter coordinates of two known vertices and select the condition (equilateral triangle or right angle at third vertex). The calculator will provide possible solutions.

5. Frequently Asked Questions (FAQ)

Q1: Why are there two solutions for equilateral triangle?
A: The third vertex can be on either side of the line connecting the two given vertices, resulting in two possible positions.

Q2: How accurate are the results?
A: Results are mathematically precise, though displayed with limited decimal places for readability.

Q3: Can I use this for 3D coordinates?
A: This calculator works for 2D coordinates only. For 3D, additional conditions would be needed.

Q4: What if I get complex number results?
A: This would mean the given conditions cannot be satisfied with the provided vertices (e.g., trying to make an equilateral triangle with colinear points).

Q5: Can this be used for other triangle types?
A: Currently supports equilateral and right-angled at third vertex. Other conditions could be added in future versions.