Three points determine a triangle: Use the distance formula to determine whether the following three points determine a line or a triangle: (-5, 2); (-2, 1); (3, -4).

To solve this we can determine the distances between the 3 pairs of points. If the points lie on a straight line, the largest distance will equal the sum of the other two distances. Otherwise the points determine a triangle.

We can use the Distance Formula on the 3 pairs of points:

For (-5, 2) and (-2, 1), the length is

For (-2, 1) and (3, -4), the length is

For (-5, 2) and (3, -4), the length is

We see that d₃ < d₁ + d₂, so the points determine a triangle.