As Pope said , if you think the graph then this problem is easy .
We know the graph of y = |x-a|+b is "V" shape and its vertex is at (a,b) ,
so the graph of y = -|x-a|+b is "∧" shape and its vertex is at (a,b) .
Therefore (2,3) is on the left segment whose slope is 1 ,
and (8,1) is on the right segment whose slope is -1 .
The equations of these segments are y=x+1 and y=-x+9 , try to find their intersection .
We can find x=4 and y=5 , so (a,b) = (4,5) .