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Geometry Translations Worksheet

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Geometry Translations Worksheet

A translation slides a shape without turning, flipping or resizing it. On a coordinate grid, the first number in a vector moves left or right; the second moves up or down. For example, (3, −2) means 3 units right and 2 units down. Add the vector to each vertex coordinate. On the grids, use the usual convention: right and up are positive.

Decode the moves

Use the examples and coordinate grids to help solve the translation clues.

1.A pattern tile slides 4 units left and 2 units up. Which vector describes the move?

(4, −2)
(−4, 2)
(−2, 4)
(2, −4)

2.A triangle has vertices A(1, 1), B(4, 1) and C(2, 3). Translate it by vector (2, 1). Write the coordinates of A′, B′ and C′.

3.On the coordinate grid you draw in the space below, plot triangle P with vertices (1, 1), (3, 1) and (2, 3). Then translate it by vector (3, 2) and plot P′. Use equally spaced grid lines with 1 unit per square, and label both triangles.

4.On the number line, a point moves from −2 to 2. What translation vector describes the move, using 0 for the vertical component?

Plan the festival pattern

A design team is creating a repeating motif for a community festival. Use translations to make the pattern line up neatly.

5.A square motif has corners (0, 0), (2, 0), (2, 2) and (0, 2). Translate it by (−3, 1). List the four new corner coordinates.

6.A motif is translated by (2, 3), then by (−1, 4). What single vector would make the same overall move? Explain how you combined the moves.

7.True or false? A translation changes a shape’s orientation.

TrueFalse

8.A rectangle has vertices (1, 2), (5, 2), (5, 4) and (1, 4). It is translated by vector (−2, −3). Find the new coordinates and explain why its side lengths stay the same.

9.Create a repeating border pattern using a triangle of your choice. First draw a coordinate grid with equally spaced grid lines and 1 unit per square. Draw a starting triangle and at least three copies, translating each copy 4 units to the right. Label the vector used each time.

10.Mere says, “A translation by (−3, 2) moves a point 3 units right and 2 units down.” Is Mere correct? Correct the description and give the new position of (4, −1).

11.A shape ends at (7, 5) after a translation by (3, −2). What were the starting coordinates?