this is all complicated to me, as I simply take on equation $y=\frac{1}{2}x-1$
$x=\frac{1}{2}x-1$, $x/2=-1$, $x=-2$ and $y=\frac{1}{2}*(-2)-1=-2$. Answer is (-2, -2) and it's A.

We want to find a point on the graph where the x-coordinate equals the y-coordinate.
In other words, we want: $x = y$

So, let's replace $y$ with $x$ in the original equation to get: $x=\frac{1}{2}x-1$

Subtract $\frac{1}{2}x$ from both sides of the equation to get: $\frac{1}{2}x=-1$

Multiply both sides of the equation by $2$ to get: $x=-2$

So, when $x=-2$, x- and y-coordinates are equal.

Answer: A