Question

Given a triangle with the following points A(5,8), B(8,3), C(2,3), determine if the triangle is scalene, isosceles, or equilateral. Give the length of each side to show proof. Round all answers to the nearest tenth.

Answer 1

By calculating the lengths of the sides of the triangle with vertices A(5,8), B(8,3), C(2,3), we found that AB and AC are approximately 5.8 units, and BC is 6.0 units, making the triangle isosceles.

Step-by-step explanation:

To determine whether the triangle with vertices A(5,8), B(8,3), C(2,3) is scalene, isosceles, or equilateral, we need to calculate the lengths of its sides using the distance formula.

The distance formula is d = √((x2 - x1)² + (y2 - y1)²), where (x1, y1) and (x2, y2) are the coordinates of two points. Let's calculate the lengths of the sides:

• Side AB: d = √((8 - 5)² + (3 - 8)²) = √(9 + 25) = √34 ≈ 5.8
• Side BC: d = √((8 - 2)² + (3 - 3)²) = √(36 + 0) = √36 = 6.0
• Side AC: d = √((5 - 2)² + (8 - 3)²) = √(9 + 25) = √34 ≈ 5.8

The lengths of the sides AB and AC are approximately the same, while BC is a different length, hence the triangle is isosceles. As proof, we have shown that sides AB and AC are approximately 5.8 units long, and side BC is exactly 6.0 units long.