Question

Triangle ABC has vertices A(3, -5), B(7, 1) and C(3, 1).

Use this information to classify it by its sides. Use the distance formula (or Pythagorean theorem) to provide mathematical evidence that supports your answer.

Answer 1

This is a right and scalene triangle with sides 4, 6 and 7.21

Step-by-step explanation:

One way to solve this problem is to locate the three points of the triangle in the Cartesian plane to have a graphical idea of this triangle. As you can see on the image, this is a rectangle triangle, therefore we can determine with the plane the length of both legs and then with the Pythagorean theorem find out the hypotenuse as follows:

`h^2 = a^2 + b^2 \\h^2 =6^2 + 4^2=36+16\\h= \sqrt 52= 7.21`

Therefore, we have a triangle with three sides of different length, and that corresponds with a scalene triangle.