A geometry translation is an isometric transformation, meaning that the original figure and the image are congruent. Translating a figure can be thought of as "sliding" the original. If the image moved left and down, the rule will be (x - __, y - __) where the blanks are the distances moved along each axis; for translations left and up: (x - __, y + __), for right and down (x + __, y - __), for right and up (x + __, y + __).
There are 4 types of transformations, three of which are isometries. One of these is a translation, so a translation is an isometry that slides or moves over the points on a figure in the same direction so let's say I gave names to my 3 vertices in this triangle let's call this a, b and c so notice if go in a clockwise direction after a follows b, after b follows c, after c follows a. When I translate this that orientation is going to stay the same. We're still going to have a then b, b then c and c then a. But how do we describe a translation of the mathematicians? Well to do that, we're going to write an expression kind of like this which says the original coordinates whatever they are x and y are being mapped on to a new image so this tells me to take every x coordinate of this triangle and add 1 to it. Tells me to take every y coordinate of this triangle and subtract 2 so you're going to use this rule to find which way you're going to translate. When you're adding to an x you'll be shifting your figure to right, when you're subtracting from x you're going toshift your figure to the left. When y is being added to you're going to shift your figure up and when y is being subtracted it'll shift your figure down, so keep that in mind when your problems that are asking you to translate an image.