you are starting at (-3, -10) and moving half of your required distance when you land at the midpoint (-1, 1). this means you want to replicate the moves you made from the endpoint to the midpoint.
looking at the x coordinates, you started at -3 and moved to -1. that means you moved to the right (or added) 2. so do that again. if you start at the midpoint x of -1 and you move two to the right again, you end up at 1. so the x coordinate of the other endpoint will be 1.
do it again for the y's. you started at -10 and moved to 1. that means you moved to the right 11 spots, or added 11. from the midpoint y of 1, add 11 and you end up at 12. so the y coordinate of the other endpoint is 12.
put it together. your other endpoint is in (x, y) form, and you found the x and y to be (1, 12).
if you did this on graph paper, it would be much more visually intuitive.