# Triangle Vertices Calculator

**Are you looking to learn how to calculate the vertices of a triangle for math? Do you have a triangle for which you would like to find the vertices?** If you answered yes to either of these questions, you are in the right place.

*Our triangle vertices calculator will help you find the coordinates of the vertices using the coordinates of the midpoints.*

**Keep reading to learn:**

- What is the vertex of a triangle;
- How to use our triangle vertices calculator; and
- How to find the vertices of a triangle using midpoints.

## What are the vertices of a triangle?

The point at which two sides of a triangle meet is called a vertex. The word used to refer to more than one vertex is vertices.

## Instructions on how to use our triangle vertices calculator

**To find the triangle's vertices $A$, $B$, and $C$**, you need to insert the $x$ and $y$ coordinates of the midpoints $D$, $E$, and $F$, and our calculator will generate the coordinates of the vertices in real-time.

## How to find the vertices of a triangle - vertices of a triangle formula

Let's look at the following problem.

A triangle has vertices $A$, $B$, and $C$. The midpoints of the sides labeled $D$, $E$, and $F$ are ($2, 3$), ($4, 3$), and ($3, 1$), respectively. **How do we go about finding the vertices using these midpoints?**

- Understand that: $D$ is ($x_1, y_1$), $E$ is ($x_2, y_2$), and $F$ is ($x_3, y_3$)
**Using the midpoint formula:**

**Find vertex $A$:**

**Substitute in the values:**

**Find vertex $B$:**

**Substitute in the values:**

**Find vertex $C$:**

**Substitute in the values:**

## Related Calculators

Here are some related calculators that may interest you:

## FAQ

### How many sides and vertices does a triangle have?

**Three.** A triangle has three sides and three vertices. The vertices are the points where the three sides of the triangle meet.

### How do I find the vertices of a triangle using the midpoints?

To find the vertices of a triangle using the midpoints we use the following steps:

- Identify the
`x`

and`y`

values of the midpoints; - Use the midpoint formula:
`A = (x₁+x₃-x₂, y₁+y₃-y₂)`

;`B = (x₁+x₂-x₃, y₁+y₂-y₃)`

;`C = (x₂+x₃-x₁, y₂+y₃-y₁)`

; - Substitute in the respective
`x`

and`y`

values; - Calculate.