Can an equilateral triangle have integer coordinates?
Table of Contents
- 1 Can an equilateral triangle have integer coordinates?
- 2 What coordinates would you use to describe an equilateral triangle in the coordinate plane?
- 3 Is an equilateral triangle as shown in the figure find the coordinates of its vertices?
- 4 What are the vertices of an equilateral triangle?
- 5 Can an equilateral triangle have all its vertices integer?
- 6 Is it possible to translate an equilateral triangle with integer coordinates?
Can an equilateral triangle have integer coordinates?
Therefore there is no equilateral triangle ABC with two vertices on the x-axis and all vertices having integer valued coordinates. Since \triangle AOC is a right triangle, the Pythagorean Theorem says that |OC|^2 + |AO|^2 = |AC|^2.
What coordinates would you use to describe an equilateral triangle in the coordinate plane?
An equilateral triangle has vertices at (0,0) and (6,0) in a coordinate plane. Triangles BAC and CAO are congruent and hence |OC| = |CB| and angle ACB is a right angle. Hence the x-coordinate of A is 3.
Can one make an equilateral triangle with all vertices at integer coordinates?
Therefore an equilateral triangle cannot have all its vertices integer coordinates.
Can you prove a triangle is an equilateral triangle?
Answer: If three sides of a triangle are equal and the measure of all three angles is equal to 60 degrees then the triangle is an equilateral triangle. The distance formula can be used to prove that a triangle is an equilateral triangle.
Is an equilateral triangle as shown in the figure find the coordinates of its vertices?
Clearly, coordinates of B and C are (1, 0) and (5, 0) respectively. As OM = 3 units and AM of A = 2√3 units, therefore, coordinates are (3,2√3).
What are the vertices of an equilateral triangle?
The vertex of an equilateral triangle is (2, – 1) and the equation of its base is x + 2y = 1 .
What are the points of an equilateral triangle?
In geometry, an equilateral triangle is a triangle in which all three sides have the same length. In the familiar Euclidean geometry, an equilateral triangle is also equiangular; that is, all three internal angles are also congruent to each other and are each 60°….
| Equilateral triangle | |
|---|---|
| Area | |
| Internal angle (degrees) | 60° |
Is there an equilateral triangle with rational points?
Let’s find out. The interesting theorem is: there is no equilateral triangle ACE where points have all rational coordinates in the Cartesian plane.
Can an equilateral triangle have all its vertices integer?
Therefore an equilateral triangle cannot have all its vertices integer coordinates. In two dimensions there’s no equilateral triangle with integer coordinates, i.e. whose vertices are lattice points. Let’s prove that. Suppose ABC is an equilateral triangle whose coordinates are integers.
Is it possible to translate an equilateral triangle with integer coordinates?
So it is not possible for and it is not possible that is an equilateral triangle. Any triangle whose vertices have integer coordinates can be translated so that one of the vertices, say , is at (0,0) and the other two vertices have integer coordinates.
How do you prove that a triangle cannot be equilateral?
If the vertices of a triangle have integral coordinates, prove that the triangle cannot be equilateral. >> If the vertices of a triang… If the vertices of a triangle have integral coordinates, prove that the triangle cannot be equilateral.
Can the coordinates of the third vertex of an equilateral triangle be rational?
If two vertices of an equilateral triangle have integral coordinates, then the third vertex will have: Therefore, both the coordinates of the third vertex cannot be rational. Was this answer helpful?