-- The distance between two points is
√[ (difference in their 'x's)² + (difference in their 'y's)² ]
-- The slope of the line that passes through two points is
(difference in their 'y's) / (difference in their 'x's) .
Now . . .
-- Take the two points 'A' and 'B'.
Find the distance between them.
Find the slope of the line passing through them.
-- Take the two points 'B' and 'C'.
Find the distance between them.
Find the slope of the line passing through them.
-- Take the two points 'A' and 'C'.
Find the distance between them.
Find the slope of the line passing through them.
Then . . .
-- Look for two of the distances that are equal.
That tells you that the triangle is 'isosceles'.
-- Look for two of the lines whose slopes are negative reciprocals.
That tells you that those two lines are perpendicular, so it's a right triangle.
