A scatterplot contains four points: (−2,−2), (−1,−1), (0,0), and (1,1). A fifth point, (2,y), is to be added to the plot. Let r represent the correlation between x and y.

a. Find the value of y so that r = 1.

b. Find the value of y so that r = 0.

c. Find the value of y so that r = 0.5.

d. Find the value of y so that r = −0.5.

e. Give a geometric argument to show that there is no value of y for which r = −1.