If the figure below is rotated 180 degrees about the origin, the new location is a’(8, 0), b’(0, -6), c’(-8, 0), d’(0, 6).

should be :)

sorry if wrong but it should be

 The triangle is a right triangle because 5²+12²= 13²  .

Step-by-step explanation:

According to the converse of Pythagoras theorem , if the square of largest side of triangle is equal to the sum of squares of other two sides, then it is a right triangle.

The given side-lengths of triangle = 5 cm, 13 cm, and 12 cm

Here , 13²= 169

and 5²+12²=25+144=169

i.e.  the square of largest side of triangle is equal to the sum of squares of other two sides.

Thus , by converse of Pythagoras theorem, we can say that it is a right triangle.

Therefore  , the correct answer : The triangle is a right triangle because 5²+12²= 13²  .