The three basic transformations: rotations, reflections and translations

This is a rotation. Usually, most rotations occur around the origin, or (0,0) on a coordinate graph. The image is "turning" around the origin, as you see here. The formula to move an image 90 degrees counterclockwise is (-y,x). You can repeat the process for 180 and 270 degrees.

This is a reflection across the line y=x. Reflections can occur across the x axis or the y axis, the lines y=x or y=-x, and any other line on a coordinate graph. Reflections "flip" an image across a line. The formula for reflections across the x axis is (x,-y). The formula for reflections across the y axis is (-x,y). The formulas for reflections across the lines y=x and y=-x are (y,x) and (-x,-y), respectively.

This is a translation with a horizontal component of 4 and a vertical component of -1. Translations simply "slide" an image from one place to another. The formula for vertical translations is (x,y+k). The formula for horizontal translations is (x+h,y). The formula for oblique translations, or translations with a horizontal and vertical component, is (x+h,y+k).

This is a dilation with a scale factor of 2. Dilations are making an image larger or smaller by multiplication. The three formulas for dilations are (rx,y) to make the image wider, (x,ry) to make the image taller, and (rx,ry) to increase its size both vertically and horizontally.