The coordinates for the vertices of a right triangle are (1, 4), (6, 4), and (6,1). what is the length of the longer leg?

We pair up the vertices given and solve for the distances between the points to determine the lengths of the sides of the triangle. 
     (1,4) and (6,4) = sqrt ((4-4)² + (6-1)²) = 5
     (6,4) and (6,1) = sqrt ((4-1)² + (6-6)²) = 3
     (6,1) and (1,4) = sqrt ((4-1)² + (6-1)²) = 5.83
The longest side is the hypotenuse, the second to the longest is the longer leg and the shortest is the smallest value. The answer therefore is 5. 

No a triangle cannot be formed because when you add the two smallest number together (which would be 11) the have to be bigger than the number it is "against" ( which would be 12)