Problem for you to solve!

Harry Potter and Hermione Granger are in Hogwarts School of Magic, standing on two opposite ends of a hallway. Their locations are plotted on a Cartesian plane as:
Harry ( 2 , 4 ) and
Hermione ( 5 , 8 )

a) Find the equation and distance of the line connecting Harry and Hermione.

b) Ron Weasly is running to class in a hallway perpendicular to the hallway that Harry and Hermione are in. What is the equation of the line of Ron's hallway if Ron passes through the point ( 4 , 6 )?

c) Find the midpoint of the line connecting Hermione and Ron.
Hermione ( 5 , 8 ) and
Ron ( 4 , 6 )

d) Outside of Hogwarts, Neville Longbottom is on a fly-away broomstick!! The broomstick's path is parallel to the line connecting Ron ( 4 , 6 ) and Hermione ( 5 , 8 ). What is the equation of the path of Neville's broomstick if it passes through the point, ( 3 , 9 )?

Solutions to the problems.

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