Geometric Transformations examples Grade 10 Math

📚 Quick Study Guide

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• Translation: A transformation that slides a figure along a straight line. Every point of the figure moves the same distance in the same direction.
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• Rotation: A transformation that turns a figure about a fixed point (the center of rotation). Defined by the angle of rotation and the direction (clockwise or counterclockwise).
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• Reflection: A transformation that flips a figure over a line (the line of reflection), creating a mirror image.
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• Dilation: A transformation that enlarges or reduces a figure by a scale factor. The center of dilation is the fixed point from which the figure is enlarged or reduced.
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• Congruence: Transformations like translation, rotation, and reflection preserve size and shape, resulting in congruent figures.
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• Similarity: Dilation changes the size but preserves the shape, resulting in similar figures.
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• Scale Factor (k): In dilation, if $k > 1$, the image is an enlargement. If $0 < k < 1$, the image is a reduction. If $k = 1$, the figure remains unchanged.

Practice Quiz

1. What type of transformation is defined by sliding a figure along a straight line?
   1. Translation
   2. Rotation
   3. Reflection
2. Which transformation creates a mirror image of a figure?
   1. Translation
   2. Reflection
   3. Dilation
3. What does a dilation with a scale factor of $k > 1$ do to a figure?
   1. Enlarges it
   2. Reduces it
   3. Leaves it unchanged
4. Which transformations always result in congruent figures?
   1. Translation, Rotation, Reflection
   2. Dilation only
   3. All transformations
5. What is the fixed point called around which a figure is turned in a rotation?
   1. Center of reflection
   2. Center of dilation
   3. Center of rotation
6. A triangle is dilated with a scale factor of 0.5. What happens to the size of the triangle?
   1. It is enlarged
   2. It is reduced
   3. It remains the same
7. Which transformation results in similar figures, but not necessarily congruent figures?
   1. Translation
   2. Reflection
   3. Dilation