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

The answer is B and Isosceles Triangle.

Explanation:

Answer 2

ABC is an isosceles triangle.

Explanation:

Given,

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

By the distance formula,

`AB=√((4-2)^2+(7-2)^2)`

`=√(2^2+5^2)`

`=√(4+25)`

`=√(29)\text{ units}`

`BC=√((6-4)^2+(2-7)^2)`

`=√(2^2+(-5)^2)`

`=√(4+25)=√(29)\text{ units}`

`CA=√((2-6)^2+(2-2)^2)`

`=√((-4)^2)=√(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,