Transformations Practice Worksheet

Transformations Practice Worksheet

Transformations are a fundamental concept in mathematics, particularly in geometry and algebra. They involve changing the position, size, or shape of a figure. In this worksheet, we will practice different types of transformations, including translations, rotations, and reflections.

Translations

A translation is a transformation that moves a figure from one position to another without changing its size or shape. It is like sliding the figure along a straight line.

📝 Note: In a translation, the image is the same size and shape as the preimage.

Let’s practice some translation problems:

• Translate the point (2, 3) by 4 units to the right and 2 units down.
• Translate the line segment with endpoints (1, 2) and (4, 6) by 3 units to the left and 1 unit up.

Solutions

• The translated point is (2 + 4, 3 - 2) = (6, 1).
• The translated line segment has endpoints (1 - 3, 2 + 1) = (-2, 3) and (4 - 3, 6 + 1) = (1, 7).

Rotations

A rotation is a transformation that turns a figure around a fixed point. It is like rotating the figure around a pivot point.

🔄 Note: In a rotation, the image is the same size and shape as the preimage.

Let’s practice some rotation problems:

• Rotate the point (3, 4) by 90° counterclockwise around the origin.
• Rotate the triangle with vertices (2, 3), (4, 5), and (6, 7) by 180° clockwise around the point (4, 5).

Solutions

• The rotated point is (-4, 3).
• The rotated triangle has vertices (-2, -3), (-4, -5), and (-6, -7).

Reflections

A reflection is a transformation that flips a figure over a line or plane. It is like reflecting the figure in a mirror.

👀 Note: In a reflection, the image is the same size and shape as the preimage.

Let’s practice some reflection problems:

• Reflect the point (2, 3) over the x-axis.
• Reflect the quadrilateral with vertices (1, 2), (3, 4), (5, 6), and (7, 8) over the line y = x.

Solutions

• The reflected point is (2, -3).
• The reflected quadrilateral has vertices (2, 1), (4, 3), (6, 5), and (8, 7).

Dilations

A dilation is a transformation that changes the size of a figure. It is like enlarging or shrinking the figure.

🔍 Note: In a dilation, the image is not the same size as the preimage.

Let’s practice some dilation problems:

• Dilate the triangle with vertices (2, 3), (4, 5), and (6, 7) by a scale factor of 2.
• Dilate the circle with center (4, 5) and radius 3 by a scale factor of ¹⁄₂.

Solutions

• The dilated triangle has vertices (4, 6), (8, 10), and (12, 14).
• The dilated circle has center (4, 5) and radius ³⁄₂.

Compositions of Transformations

A composition of transformations is a combination of two or more transformations.

🤝 Note: The order of the transformations matters.

Let’s practice some composition problems:

• Translate the point (2, 3) by 4 units to the right and then rotate it by 90° counterclockwise around the origin.
• Reflect the triangle with vertices (2, 3), (4, 5), and (6, 7) over the x-axis and then dilate it by a scale factor of 2.

Solutions

• The translated point is (2 + 4, 3) = (6, 3). The rotated point is (-3, 6).
• The reflected triangle has vertices (2, -3), (4, -5), and (6, -7). The dilated triangle has vertices (4, -6), (8, -10), and (12, -14).

Now that we have practiced different types of transformations, let’s summarize what we have learned.

Transformations are a fundamental concept in mathematics that involve changing the position, size, or shape of a figure. We can perform translations, rotations, reflections, and dilations to transform a figure. We can also combine these transformations to create a composition of transformations. By understanding transformations, we can better understand the world around us and develop problem-solving skills.

Related Terms:

• Transformation Worksheet pdf
• Translation Worksheet
• Worksheet transformations geometry
• IGCSE transformation worksheet pdf
• Rotation worksheet
• Reflection worksheet