Pre-cal math question?

Question

Find the midpoint of each diagonal of a square with side of length s. Draw the conclusion that the diagonals of a square intersect. Use (0,0), (0,s), (s,0), and (s, s) as the vertices.

The answer in the back of the book says midpoint1 = (s/2, s/2) midpoint 2= (s/2, s/2). I know that you have to use the midpoint formula and the distance formula, but I don't know how to do it with variables.

Answer 1

midpoint = [ (x1 + x2) / 2 , (y1 + y2) / 2 ]

(0,0) and (s, s) form one diagonal

midpoint1 = [ (0 + s) / 2 , (0 + s) / 2 ] = (s/2, s/2)

(0,s) and (s, 0) form the other diagonal

midpoint2 = [ (0 + s) / 2 , (s + 0) / 2 ] = (s/2, s/2)

distance formula would be use to find the difference between two points

for example (0,0) and (s,s)

√[ (x2-x1)² + (y2-y1)² ] = √[ (s-0)² + (s-0)² ] = √(2s²) = √(2)s