Question

"Using the distance formula for the triangle with vertices W(-5,5), X(7,4), and Y(-1,-5), classify the triangle by its sides."

Option a) Equilateral Triangle
Option b) Isosceles Triangle
Option c) Scalene Triangle
Option d) Not a triangle

Answer 1

The triangle is classified as an Isosceles Triangle.

Step-by-step explanation:

To classify the triangle by its sides, we can use the distance formula to find the lengths of the three sides of the triangle. The distance formula is given by:

d = √((x2 - x1)² + (y2 - y1)²)

Using the given coordinates of the vertices, we can calculate the distances between them:

1. d(WX) = √((-5 - 7)² + (5 - 4)²) = √(12² + 1²) = √(144 + 1) = √145
2. d(WY) = √((-5 - (-1))² + (5 - (-5))²) = √((-4)² + 10²) = √(16 + 100) = √116
3. d(XY) = √((7 - (-1))² + (4 - (-5))²) = √((8)² + (9)²) = √(64 + 81) = √145

Comparing the lengths of the sides, we see that the triangle has two sides with the same length, d(WX) and d(XY), and one side with a different length, d(WY). Therefore, the triangle is classified as an Isosceles Triangle.