Based on your description of the eleven points plotted in a diagonal pattern in the first quadrant of a coordinate plane, showing an increasing trend, the best estimated correlation coefficient would be 0.9.
This indicates a strong positive correlation, meaning that as one variable increases, the other variable also tends to increase. A correlation coefficient of 1 would imply a perfect linear relationship, but since you mentioned that the points show an increasing trend rather than perfect alignment, 0.9 is a more appropriate choice.
So the answer is 0.9.