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Shape Transformations Worksheet

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Shape Transformations Worksheet

Use the coordinate rules to solve each task. For the plotting task, draw the grid as instructed. Coordinates are written (x, y). A prime (′) labels an image point after a transformation.

Transformation clues

A design team is building a repeating floor pattern. Identify how each move changes a shape.

1.Match each transformation to its description: translation, reflection, rotation. Descriptions: (a) turn around a fixed point; (b) slide without turning or flipping; (c) flip across a line.

Translation
Reflection
Rotation

Flip across a line
Slide without turning or flipping
Turn around a fixed point

2.A rigid transformation is a translation, reflection or rotation. Select every property that stays unchanged: side lengths, angle sizes, position on the plane, area.

Side lengths
Angle sizes
Position on the plane
Area

Follow the coordinates

Apply each rule to every vertex. Keep the vertex labels in the same order.

3.Triangle ABC has vertices A(3, 2), B(5, 2) and C(4, 4). Translate it by vector (−2, 3). Find A′, B′ and C′.

4.Square PQRS has P(1, 1), Q(3, 1), R(3, 3) and S(1, 3). Reflect the square across the y-axis. Give the four image coordinates.

5.Draw coordinate axes with a grid covering at least −4 to 4 on both axes. Plot triangle ABC at A(2, 1), B(4, 3) and C(2, 5). Then rotate it 180° about the origin and plot A′B′C′. Write the image coordinates.

6.Triangle DEF has D(−3, 2), E(−1, 2), F(−2, 4). Its image has D′(3, 2), E′(1, 2), F′(2, 4). Name the transformation and state its mirror line or centre.

Transformation trail

A pattern is made by carrying out transformations in the stated order. Do not skip a step.

7.Rectangle WXYZ has W(1, 2), X(4, 2), Y(4, 4), Z(1, 4). First translate by (3, −1), then reflect across the x-axis. Find all coordinates after the translation and all final coordinates.

8.A designer rotates a point at (5, −1) by 270° clockwise about the origin, then translates it by (−2, 4). What are its final coordinates?

9.A student says, “A reflection changes a shape’s area because it flips the shape.” Is the student correct? Explain why translations, reflections and rotations preserve area.