The x-coordinate of the point will be 1 + (5/7)(8-1) = 6.
This is because you start out with the original x-coordinate at point A, which is 1. Then you add the result you get from multiplying the distance between x-coordinates (8-1) by 5/7, which is from the ratio 5:2. There are 5 parts out of the 7 parts (7 parts because 5+2).
The y-coordinate of the point will be 2 + (5/7)(16-2) = 12
This is because you start out with the y-coordinate of point A, which is 2. Then you add the result you get by multipling the distance between y-coordinates by 5/7.
