baseball home plate?

It depends. The back line of the catcher's box is eight feet behind the plate. The midpoint of the length of the batter's box (which is 6 feet) is 8.5 inches behind the front of the plate.

The catcher cannot catch a pitch while having any part of his body, including his glove, over any part of the plate.

I agree. anyone who answered 45+ feet obviously didn't read the question. The catcher gets as close to the plate as he can to give the pitcher the best target. However, he cannot be over the plate and cannot interfere with the swing of the batter. The batter is allowed to stand anywhere in the batters box, and where varies from batter to batter.

From the catcher to the batter??

There is no specific answer for that. Batters and catchers set up in different parts of the batter's box and the catcher's box on every pitch.

There are too many variables with each pitch...catchers move inside and closer to a batter when a pitcher wants to jam the batter and outside when they batter has a long swing that they want to manipulate.

Batters often try to move in and out and up and down in the box as a way of adjusting to the pitch and shortening up their swing.

I hope that helps.

From the catcher to the batter?

That depends on where the catcher sets up for the next pitch.

There is both a batter's box (actually two - one for each of left and right handed batters) and there is a catcher's box. Each has prescribed shapes and sizes and a prescribed relationship to one another. The batter can stand anywhere within the box on his side of the plate, and the catcher can crouch anywhere within his box. So, there is no direct answer to your question.

Diagram 2 in each of chapter one and chapter three of the rulebook shows the dimensions and angles of the whole infield.

i think it pretty much depends on where the catcher sets up. I don't believe there is a set lengh w/ catchers, there are the chaulk lines that hitters must stay in, but both hitters and catchers obliterate those lines and are all over the place usually. I noticed at a game last year that Travis Hafner always rubs oyt the line and stands WAY back in the box. I remember thinking I would NOT wanna be the catcher, he seems like he was gonna clobber him on his follow through with that huge donkey swing of his!

Short answer: they are both all over the place and there is no set distance.

Generally, they are far enough apart that the batter can hold the bat full-length with one hand and swing an arc such that the bat just misses the catcher's body when the catcher is in a normal catching position.

60 Feet 6 Inches...give or take a few where the catcher sets up.

The batter six is six feet long. So if the batter is in front it's a max of six feet

It depends on where they stand. Have you ever played baseball before?