Question

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 1

Answer:

The answer is B and Isosceles Triangle.

Step-by-step explanation:

Answer 2

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,

$AB=\sqrt{(4-2)^2+(7-2)^2}$

$=\sqrt{2^2+5^2}$

$=\sqrt{4+25}$

$=\sqrt{29}\text{ units}$

$BC=\sqrt{(6-4)^2+(2-7)^2}$

$=\sqrt{2^2+(-5)^2}$

$=\sqrt{4+25}=\sqrt{29}\text{ units}$

$CA=\sqrt{(2-6)^2+(2-2)^2}$

$=\sqrt{(-4)^2}=\sqrt{16}=4\text{ units}$

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,