You can't really say how far a constellation is. A constellation is just a group of stars, and even though the stars in a constellation look close together in the sky, in reality they might be very far from each other. Some of the stars could be relatively close to us, and some much farther away.
Really, the only question you can answer is how far from earth is each individual star in Perseus is.
Any constellation is a group of stars that appear to form some kind of pattern, but have no connection with each other. They all happen to be in roughly the same direction from us, but they're all at different distances. So there's no such thing as a constellation's distance from us.
Some of the stars in the constellation Perseus include Algol, Mirfak, and Atik.
The constellation Grus is approximately 17.08 light-years away from Earth.
If you mean the constellation cancer, there is no such thing as a "distance to a constellation". It just doesn't make sense. A constellation is basically a general direction in space.
fairly big
Any constellation is a group of stars that appear to form some kind of pattern, but have no connection with each other. They all happen to be in roughly the same direction from us, but they're all at different distances. So there's no such thing as a constellation's distance from us.
Perseus is a constellation ... a collection of individual stars that appear to form a pattern in the sky because of their positions. The stars of a constellation have no connection or association with each other. Each one has its own individual color, temperature, size, and distance from our solar system.
Please bear in mind that a constellation (such as Perseus) is basically a direction in the sky. It really doesn't make much sense to talk about the distance from such a direction (which is a direction from our point of view), to some object. If you mean the asterism (the group of stars), the main stars of Perseus - or any other constellation - happen to be more or less in the same direction, but the distance from these stars to Earth vary quite a lot.
Beta is not a constellation.
Perseus became a constellation when he cut off Medusa's head and saved Princess Andromeda.
At night....
Perseus
Some of the stars in the constellation Perseus include Algol, Mirfak, and Atik.
The constellation Grus is approximately 17.08 light-years away from Earth.
Greek philosophers/astronomers thought that the constellation "perseus" looked like a human shape, and since "perseus" was a famous Greek hero, they named it after him.
If you mean the constellation cancer, there is no such thing as a "distance to a constellation". It just doesn't make sense. A constellation is basically a general direction in space.
Constellations such as Perseus have been known since antiquity. No one knows who first named Perseus, let along who first recognized that group of stars as a single constellation.