Show that the points (-2, 3), (8, 3), and (6, 7) are the vertices of a right triangle.

Given coordinates of triangle A(-2, 3), B(8, 3), and C(6, 7)
AB = √[8 - (-2)]² + (3 - 3)² = √(10)² + (0)² = √100
AC = √[6 - (-2)]² + (7 - 3)² = √(8)² + (4)² = √64 + 16 = √80
BC = √(6 - 8)² + [7 - (3)]² = √(-2)² + (4)² = √4 + 16 = √20
If ABC is a right-angled triangle, then the square of one side must be equal to the sum of the squares of the other two sides.
AB² = (√100)² = 100
and AC² + BC² = (√80)² + (√20)² = 100
∴ AB² = AC² + BC²
Thus, the triangle satisfies the Pythagoras theorem.
Hence, the triangle is a right-angled triangle.