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2D Shape Transformations

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2D Shape Transformations

Use the coordinate grid to explore translations, reflections and rotations. Coordinates are written as (x, y). For rotations, unless stated otherwise, turn around the origin (0, 0).

Spot the transformation

A transformation moves or changes the orientation of a shape. The shape's size and form stay the same.

1.Match each transformation to what it does: translation; reflection; rotation. Descriptions: a) turns around a point, b) slides without turning, c) flips over a line.

Translation
Reflection
Rotation

Flips over a line
Slides without turning
Turns around a point

2.A robot-shaped triangle has vertices A(1, 1), B(4, 1) and C(2, 3). It slides 2 units left and 3 units up. Write the new coordinates of A, B and C.

3.A point P is at (5, -2). Reflect it across the y-axis. What are the coordinates of P′?

(-5, -2)
(5, 2)
(-5, 2)
(2, -5)

4.A reflection across the x-axis changes the x-coordinate but leaves the y-coordinate unchanged. Is this statement true or false?

Turn and flip

Keep track of the order and direction of every move. A clockwise turn follows the direction of a clock's hands.

5.A square has vertices A(1, 1), B(3, 1), C(3, 3) and D(1, 3). Rotate it 90° clockwise around the origin. Give the coordinates of A′, B′, C′ and D′.

6.A point starts at (4, 2). First translate it 3 units left. Then reflect the new point across the y-axis. Where does it finish?

7.A rectangle is reflected. Select the one correct combination of properties that stay the same: A) side lengths, area and shape; B) side lengths, area and orientation; C) area, orientation and shape; D) side lengths, orientation and shape.

A) Side lengths, area and shape
B) Side lengths, area and orientation
C) Area, orientation and shape
D) Side lengths, orientation and shape

8.Point R starts at (-2, 5) and ends at (3, 5). What translation takes R to its new position?

9.Plot triangle P(-4, 1), Q(-2, 1) and R(-3, 4) on the coordinate grid. Reflect it across the y-axis and write the new vertices.

10.A friend says, “A rotation and a reflection are the same because both move a shape.” Explain how the two transformations are different. Include one example of each.