Determine whether the three points are the vertices of a right triangle. (6, -6), (9, -6), (9, 1)

The three given points are the vertices of a right triangle.

Step-by-step explanation:

To determine that the three points are the vertices of a right triangle let us find the distance between each two points

The formula of the distance is

∵ = 6 and = -6

∵ = 9 and = -6

∴ =

∴ = 3

∵ = 6 and = -6

∵ = 9 and = 1

∴ =

∴ =

∵ = 9 and = 1

∵ = 9 and = -6

∴ =

∴ = 7

Let us use the fact that if the square of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle at the vertex which opposite to the longest side

∵ The longest side is

∵ The other two sides are 3 and 7

∵ ( )² = 58

∵ (3)² + (7)² = 9 + 49 = 58

∴  ( )² = (3)² + (7)²

- By using the fact above

∴ The triangle is a right triangle

The three given points are the vertices of a right triangle.