Exploring Same Standard Deviation

Drag any of the blue dots around. You can control the x and y coordinates for any point except the diamond: the y-values are determined by the computer to ensure the y standard deviation is the same as the x standard deviation. Thanks to the squaring, there are actually two y-values which are valid for your choice of x-value -- use the checkbox to switch between them. The "Mixed Products" represent the numerator for the formula for r: Keeping the x and y values constant, and simply changing the order they are paired with each other, will only effect the numerator of this equation. Therefore, the closer to zero you can get the "Mixed Products", the worse your correlation will be.
Algebra Challenge: How does the computer work out the y-value for the diamond point?