Correlation of the Vertices of a Triangle

The figure below is a simpler version of the original problem posed to my students. The vertices of Triangle ABC are my points if interest. Drag point A slowly in order to find other locations for point A such that the correlation of points A, B, and C remains zero. When you find a point, click on the Capture Point button. I have included the Standardized Triangle as well. What do you think is true about this triangle when the correlation is zero? What patterns do you notice about all possible locations of point A that produce a correlation of zero?