Triangle ABC has vertices at A(2 , 2), B(4, 7), and C(6, 2). Classify the triangle according to the side lengths. A) equilateral B) isosceles C) right D) scalene

Answer :

iancar715

Answer:

The answer is B and Isosceles Triangle.

Step-by-step explanation:

Answer:

ABC is an isosceles triangle.

Step-by-step explanation:

Given,

The triangle ABC has vertices at A(2 , 2), B(4, 7), and C(6, 2).

By the distance formula,

[tex]AB=\sqrt{(4-2)^2+(7-2)^2}[/tex]

[tex]=\sqrt{2^2+5^2}[/tex]

[tex]=\sqrt{4+25}[/tex]

[tex]=\sqrt{29}\text{ units}[/tex]

[tex]BC=\sqrt{(6-4)^2+(2-7)^2}[/tex]

[tex]=\sqrt{2^2+(-5)^2}[/tex]

[tex]=\sqrt{4+25}=\sqrt{29}\text{ units}[/tex]

[tex]CA=\sqrt{(2-6)^2+(2-2)^2}[/tex]

[tex]=\sqrt{(-4)^2}=\sqrt{16}=4\text{ units}[/tex]

Since, AB = BC ≠ CA

ABC is not an equilateral triangle,

AB = BC ⇒ ABC is an isosceles triangle.

ABC is not a scalene triangle.

AB² + BC² ≠ CA² or AB² + CA² ≠ BC²  or CA² + BC² ≠ AB²

ABC is not a right triangle,

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