I may be simple minded but when I want to hang a mirror in the bathroom, I simply decide how high I need the mirror to go. Then I center it on the wall, carefully judging the distance on either side and when it looks like it is in the right place, I hang it.
My DH looks at this task in a slightly different way. And, for someone who hates math and spacial issues, he certainly tortures himself in hanging a mirror (or picture for that matter).
Case in point. There was no mirror over the sink in the bathroom of my new apartment. Go figure? I had purchased a mirror that I thought would do nicely. I thought the unique finish would go well with the granite on the counter. It was a good size but not so God awful heavy that hanging it was going to be a chore and I would always fear it falling from the wall taking a good chunk of sheet rock with it.
Naturally my DH's first comments upon seeing the mirror were, "Do you realize how ugly that thing is?" and "This isn't heavy enough. A decent mirror is always heavy."
So be it. Moving on . . .
He pulled out his tool box, his cordless drill, his cordless screwdriver, two levels, a hammer, a rubber mallet, a regular screwdriver, and a pencil. We commenced.
First he asked me how high I wanted it above the counter. When I showed him, he asked for the exact measurement. "Why do you need that? A half inch or so either way won't matter."
"I need the exact distance so I can hang this correctly." And from this he proceeded - and, no, I could not make this up. He asked me to measure the width of the counter, I said it was 34 inches, so 17 inches would be the exact middle. He remeasured and determined that I was incorrect, the counter was 34 and 3/16's, so 17 was not the true center and major math would need to be done to establish this exact point.
Once the center was marked, he marked lateral points that bisected the exact height of the mirror. A line was drawn from the furthest right point to the furthest left point. This line was then checked with a level to ensure the line was straight. When that was confirmed, he used a second level (I kid you not) because he questioned the first levels accuracy. Naturally I asked why he used the first one. The look I got told me I would never understand the logic.
Then three points were measured nine inches below the straight line. And those three points were connected by a new line that, yes, was then checked by the first, then the second level. Math was done to establish three equidistant points on the lower line. Then two points were chosen in the precise middle between points 1 and 2 and then between points 2 and 3. These final points were where the hangers were nailed into the wall.
When we stepped back and admired the new mirror, my DH asked if I was sure I did not want it higher. I assured him it looked just fine. Then we moved to hanging a new towel bar. Of course this came with a template that complicated everything given it is measured out for you. You only needed to place the template on the wall at the selected sight and use a level to make it is even. Then use a second level . . .