The above is true, however, it is best to do it with your video camera using the format card option from the menu. It does a cleaner erase than just deleting the pictures.
You camera should offer the option to delete individual photos or the entire memory card. Otherwise when you download the photos to your computer you are usually asked after the transfer if you want to remove the copied items from the memory card. If you program doesn't ask you can download for free adobe photo shop and this program will let you remove the items.
Thank you both for your answers, I will try it first with the camcorder.