A translation, or when you slide an image, is determined by distance and direction. Ex. when you have (x,y) and you have to move it (3,5) you would take the image coordinates and add 3 to the x and 5 to the y, (x+a,y+k).
A rotation, is when you turn the image but do not effect the size or shape, and is determined by the center of rotation and an angle of a rotation. Ex. if you needed to rotate the image 90 degrees clockwise you would just turn the whole picture to the right (clockwise) or you could use (x,y) = (-y,x).
A line reflection is determined by a line which you reflect over like a mirror. Ex. when you need to reflect over the y axis you would take the original coordinate (x,y) and flip it over the y axis which would make the x value the opposite, (x,y) = (-x,y).
A Size transformation is when you increase or decrease the size of the image by having a magnitude to multiply by. Ex. with a magnitude of 2 you would multiply x and y by 2 like this, (2x,2y).