Larissa is writing a coordinate proof to show that the diagnosis of a square are perpendicular to each other. she starts by assigning coordinates as given ?

The answer is show that the slope of line SQ is 1 and the slope of line PR is -1.

Suppose a square has the following coordinates (0,0), (a, 0), (0, a), and (a,a). 
The diagonals are distinct by (0,0) to (a,a) and (a,0) to (0,a) 
The slope from (0,0) to (a,a) = (a - 0)/(a - 0) = a/a = 1 The slope from (a,0) to (0,a) = (0 - a)/(a - 0) = -a/a = -1 
Two lines are thought to be perpendicular when their slopes are negative reverses of each other. In math, m2 = -1/m1 
1 = -1/-1, thus these two lines, the diagonals of the square, are perpendicular.