contestada

If A(1,2), B(5,-4) and (-3,2) are the vertices of a triangle, which statement holds true?
A. Triangle ABC is scalene because all side lengths of the triangle are different.
B. Triangle ABC is isosceles because two sides of the triangle are equal in length.
C. Triangle ABC is equilateral because all sides of the triangle are equal in length.
D. Triangle ABC is acute because all angles of the triangle are acute angles.

If A12 B54 and 32 are the vertices of a triangle which statement holds true A Triangle ABC is scalene because all side lengths of the triangle are different B T class=

Respuesta :

Medunno13

Answer: A

Step-by-step explanation:

Using the distance formula,

[tex]AB=\sqrt{(5-1)^{2}+(-4-2)^{2}}=\sqrt{16+36}=2\sqrt{13}\\BC=\sqrt{(-3-5)^{2}+(-4-2)^{2}}=\sqrt{64+36}=10\\AC=\sqrt{(-3-1)^{2}+(2-2)^{2}}=4[/tex]

From this, we can conclude that ABC is scalene.

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The correct option is A.

What is a triangle?

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.

The length of different sides are:

[tex]AB = \sqrt{(5-1)^2+(-4-2)^2} = \sqrt{16+36} = \sqrt{52}\rm\ units[/tex]

[tex]BC = \sqrt{(-3-5)^2+(2+4)^2} = \sqrt{64+36} = 10\rm\ units[/tex]

[tex]AC = \sqrt{(2-2)^2+(-3-1)^2} = \sqrt{16} = 4\rm\ units[/tex]

Since the length of all the sides of the triangle is not equal it is a scalene triangle.

Hence, the correct option is A.

Learn more about Triangle:

https://brainly.com/question/2773823

#SPJ1

Otras preguntas