Mastering Translations on the Coordinate Plane: A Step-by-Step

A translation slides every point of a figure the same distance in the same direction. On the coordinate plane you add a fixed amount to each x-coordinate and each y-coordinate, and the figure keeps its size, shape, and orientation.

• Identify the Starting Point: If you’re translating a single point, note its coordinates. For a shape, identify all the vertex coordinates.
• Apply the Vector: Add the vector’s x-coordinate to the x-coordinates of your points and the vector’s y-coordinate to the y-coordinates.
• Plot the Translated Point or Shape: Once the new coordinates are found, plot them on the coordinate plane.

Worked examples: translating a figure on the coordinate plane

Practice Questions:

1. Translate the point ( E(3,4) ) using the vector ( (-2, 1) ). What is the new coordinate?
2. Given a rectangle with vertices ( F(1,1), G(4,1), H(4,3), ) and ( I(1,3) ), translate it using vector ( (3, 0) ). What are the new vertex coordinates?

1. ( E'(1,5) )
2. ( F'(4,1), G'(7,1), H'(7,3), ) and ( I'(4,3) ).

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