Three points determine a line: Determine if the following three points determine a straight line or a triangle: (-3, -2); (1, 1); (9, 7).

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

For (1, 1) and (9, 7), the length is

For (-3, -2) and (9, 7), the length is

We see that d₃ = d₁ + d₂, so the points lie on a line.