How to Translate Shapes in Algebra
- 1). Write down the coordinates of each point in the polygon, such that the coordinates are listed as pairs of numbers in a column. For example, you would list the points of a 2 x 2 square with its lower left corner on the origin (where the axes intersect) like this: (0,0), (2,0), (2,2), (0,2). These are the points taken in a counterclockwise direction, although the order doesn't matter.
- 2). Write two values, A and B, with which to translate each point. Technically, every point on the plane is a translation of every other point, but the important part is preserving the distances between those points. To do this, write a second column of coordinates to the right of the first column. Each x-value in the second column is equal to A plus a corresponding value in the first column; each Y value in the second column is equal to B plus a corresponding value in the first column. If A = 3 and B = 2, then the second column consists of: (3,2), (5,2), (5,4), (3,4).
- 3). Draw a point on the graph corresponding to each coordinate in the second column. To find point (3,2), for example, move three units right and two units up. Connect the points together to form a shape congruent to the first one: since your original shape was a square, you will connect your four points so as to form another square. Check your shapes by finding their area; both shapes are squares with an area of 4, so they are translations of one another.
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