Question

If A(1,2), B(5,-4) and (-3,2) are the vertices of a triangle, which statement holds true?

Answer 1

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:

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

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

$AC = \sqrt{(2-2)^2+(-3-1)^2} = \sqrt{16} = 4\rm\ units$

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:

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Answer 2

Answer: A

Step-by-step explanation:

Using the distance formula,

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

From this, we can conclude that ABC is scalene.