Dilations and scale factors are important concepts in geometry that involve resizing and transforming figures. It is essential for students to practice and master these skills to confidently tackle more complex problems. The following worksheet answer key provides solutions to independent practice questions related to dilations and scale factors.
1. A dilation with a scale factor of 2 centered at the origin is applied to triangle ABC. If the coordinates of the vertices of the original triangle are A(1, 3), B(4, 5), and C(2, 7), what are the coordinates of the vertices of the dilated triangle?
Dilations And Scale Factors Independent Practice Worksheet Answer Key
Answer: A'(2, 6), B'(8, 10), C'(4, 14)
2. If a square with side length 4 is dilated by a scale factor of 3 centered at the point (0, 0), what is the side length of the dilated square?
Answer: 12
3. A rectangle has a length of 6 units and a width of 3 units. If the rectangle is dilated by a scale factor of 0.5 centered at the origin, what are the dimensions of the dilated rectangle?
Answer: Length = 3 units, Width = 1.5 units
4. Triangle XYZ is dilated by a scale factor of 1.5 centered at point P. If the original coordinates of the vertices of triangle XYZ are X(2, 4), Y(5, 6), and Z(3, 8), what are the coordinates of the dilated triangle?
Answer: X'(3, 6), Y'(7.5, 9), Z'(4.5, 12)
Practicing with these types of problems will help students develop a better understanding of dilations and scale factors, allowing them to confidently approach similar questions in the future. By mastering these fundamental concepts, students can build a solid foundation for more advanced geometry topics.
In conclusion, the Dilations And Scale Factors Independent Practice Worksheet Answer Key serves as a valuable resource for students looking to strengthen their skills in geometry. By providing solutions to practice problems, students can check their work and gain a deeper understanding of dilations and scale factors. This worksheet answer key is a useful tool for both teachers and students alike in the study of geometry.