Triangle Vertices Calculator

Created by Adena Benn
Reviewed by Aleksandra ZajΔ…c, MD
Last updated: Jun 03, 2022

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 AA, BB, and CC, you need to insert the xx and yy coordinates of the midpoints DD, EE, and FF, 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 AA, BB, and CC. The midpoints of the sides labeled DD, EE, and FF are (2,32, 3), (4,34, 3), and (3,13, 1), respectively. How do we go about finding the vertices using these midpoints?

  1. Understand that: DD is (x1,y1x_1, y_1), EE is (x2,y2x_2, y_2), and FF is (x3,y3x_3, y_3)
  2. Using the midpoint formula:
    Find vertex AA:
A=(x1+x3βˆ’x2,y1+y3βˆ’y2)A = (x_1+ x_3 - x_2, y_1 + y_3-y_2)

Substitute in the values:

A=(2+3βˆ’4,3+1βˆ’3)A = (2+ 3 - 4, 3 + 1-3)
A=(1,1)A = (1,1)
  1. Find vertex BB:
B=(x1+x2βˆ’x3,y1+y2βˆ’y3)B = (x_1+x_2-x_3, y_1+y_2-y3)

Substitute in the values:

B=(2+4βˆ’3,3+3βˆ’1)B = (2+4-3, 3+3-1)
B=(3,5)B = (3,5)
  1. Find vertex CC:
C=(x2+x3βˆ’x1,y2+y3βˆ’y1)C = (x_2+x_3-x_1, y_2 + y_3 -y_1)

Substitute in the values:

C=(4+3βˆ’2,3+1βˆ’3)C = (4 + 3 -2, 3 + 1 - 3)
C=(5,1)C = (5, 1)

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:

  1. Identify the x and y values of the midpoints;
  2. Use the midpoint formula: A = (x_1+ x_3 - x_2, y_1 + y_3-y_2); B = (x_1+x_2-x_3, y_1+y_2-y3); C = (x_2+x_3-x_1, y_2 + y_3 -y_1);
  3. Substitute in the respective x and y values;
  4. Calculate.
Adena Benn
Triangle vertices calculator.
Midpoint D
X1
Y1
Midpoint E
X2
Y2
Midpoint F
X3
Y3
Vertex A
X
Y
Vertex B
X
Y
Vertex C
X
Y
Check out 17 similar triangle calculators πŸ”Ί
30 60 90 triangle45 45 90 triangleArea of a right triangle… 14 more
People also viewed…

Base of a triangle

The base of a triangle calculator as indicated by the name determines the base of a triangle using a simple formula.

Books vs e-Books

The books vs e-books calculator answers the question: how ecological is your e-book reader? πŸ“š

Circumference

Use this free circumference calculator to find the area, circumference and diameter of a circle.

General to standard form of a circle

Our general to standard form of a circle calculator is just what you need to help you to convert the equation for the general form of a circle to the standard form of the circle.
Omni Calculator
Copyright by Omni Calculator sp. z o.o.
Privacy policy & cookies
main background