Answer
$(3,1)$ and $(5,3)$
Work Step by Step
Let's note the two points $A(x_1,y_1)$ and $B(x_2,y_2)$.
Find the midpoint of the line segment using $A(x_1,y_1)$, $B(x_2,y_2)$:
$$\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)=(4,2)$$
We write the system of equations:
$$\begin{align*}
x_1+x_2&=8\\
y_1+y_2&=4.
\end{align*}$$
Because the points $A$ and $B$ are not on the lines $x=4$ or $y=2$, it means that we have:
$$x_1\not=4; x_2\not=4, y_1\not=2, y_2\not=2.$$
We give $x_1$ and $y_1$ random values so that $x_1\not=4$ and $y_1\not=2$ and calculate $x_2$ and $y_2$:
$$x_1=3\Rightarrow x_2=8-3=5$$
$$y_1=1\Rightarrow y_2=4-1=3.$$
The points are $(3,1)$ and $(5,3)$.
