Grade 12 Math: Scale Factor Worksheet
A Grade 12 math worksheet focusing on understanding and applying scale factors in geometric transformations and real-world problems.
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Grade 12 Math: Scale Factor
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Read each question carefully and answer to the best of your ability. Show all your work for full credit.
1. A square with side length 5 cm is dilated by a scale factor of 3. What is the area of the new square?
25 cm²
45 cm²
75 cm²
225 cm²
2. If a figure is dilated by a scale factor of 0.5, what can be said about the resulting image?
It is larger than the original.
It is smaller than the original.
It is congruent to the original.
It is rotated from the original.
3. The ratio of corresponding side lengths between two similar figures is called the .
4. If a dilation has a scale factor greater than 1, the image is an .
5. A rectangle has dimensions 8 cm by 12 cm. It is dilated to create a new rectangle with dimensions 20 cm by 30 cm. What is the scale factor of the dilation?
6. Triangle ABC has vertices A(1,2), B(3,1), and C(2,4). If it is dilated from the origin by a scale factor of 2, what are the new coordinates of the vertices?
7. A scale factor of -2 would result in an image that is both larger and reflected.
True
False
8. If two figures are congruent, their scale factor is always 1.
True
False
9. A map has a scale of 1:50,000. If two cities are 10 cm apart on the map, what is the actual distance between the cities in kilometers?
10. Consider a cube with side length 's'. If the cube is dilated by a scale factor 'k', explain how the volume of the new cube relates to the volume of the original cube.