Question

Classify the triangle based on its side lengths A(2,3), B(5,-1), C(8,3).

a) Equilateral
b) Isosceles
c) Scalene
d) Right

Answer 1

The triangle with side lengths A(2,3), B(5,-1), C(8,3) is classified as a scalene triangle.

Step-by-step explanation:

To classify the triangle based on its side lengths, we need to compare the lengths of the three sides. Using the distance formula, we can calculate the lengths of AB, BC, and AC. AB = √[(5 - 2)² + (-1 - 3)²] = √[(3)² + (-4)²] = √[9 + 16] = √25 = 5. BC = √[(8 - 5)² + (3 - (-1))²] = √[(3)² + (4)²] = √[9 + 16] = √25 = 5. AC = √[(8 - 2)² + (3 - 3)²] = √[(6)² + (0)²] = √36 = 6.

Since all three sides have different lengths, the triangle is classified as a scalene triangle.