Answer
$(2,3)$ and $(4,1)$
Work Step by Step
Step 1. Points that are $\sqrt {10}$ units from $(1,0)$ are on a circle: $(x-1)^2+(y)^2=10$
Step 2. Points that are $\sqrt {10}$ units from $(5,4)$ are on a circle: $(x-5)^2+(y-4)^2=10$
Step 3. Graph the two circles as shown in the figure and identify the intersects as $(2,3)$ and $(4,1)$
One can also solve the system of equations from step 1 and 2 to get the same results.
