Question

Do the points (3,2),(-2,-3),and (2,3) form a triangle? If so, name type of triangle formed.

Answer 1

We get this by Pythagoras' theorem, e.g. AB² = (3 -(-2))² + (2 -(-3))² 

so AB² = 50. Similarly, AC² = 1² + 1² = 2², so right away we see that the triangle isn't equilateral. Meanwhile BC² = (-2 -2)² + (-3 -3)² = 16 + 36 = 52 - sightly more than AB². So it's not isosceles either. 

Finally, we should check to see if it's right-angled. 

The vector AB is (-5, -5); AC is (-1, 1); and BC = (4, 6). 

Notice that AB and AC are indeed perpendicular, meaning that the triangle has a right angle at A.