Questions and Answers
If A is (0,3) and A' is (0,33), what is the scale factor?
11
Triangle A has sides 3, 4, and 5. Triangle A' has sides 12, 16, and 20. What is the scale factor?
4
Line segment AB is 4 units long, and line segment AB' is 1 unit long. What is the scale factor?
1/4
If A' is the image dilated by a scale factor of 3, and A' is (27, 9), what is the x-value of A?
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What is the scale factor expressed by the algebraic representation (2.5x, 2.5y)?
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What is the scale factor expressed by the algebraic representation (6x, 6y)?
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If a square with a perimeter of 4 inches is dilated by a scale factor of 2, what would be the new perimeter of the image?
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At which scale factor will the pre-image and image be congruent?
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Triangle A has a vertex (4,5). Triangle A' has a vertex (12, 15). What is the scale factor?
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The algebraic representation of a dilation is expressed as (2/3x, 2/3y). What is the scale factor?
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If A (-2, 4) is dilated by a scale factor of 4, what is the new x-value of A'?
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If A (-6, 3) is dilated by a scale factor of 1/12, what is the new x-value of A'?
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If A (0, -12) is dilated by a scale factor of 1/3, what is the new y-value of A'?
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Find the scale factor of this dilation.
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If a dilation is represented algebraically as (1/6x, 1/6y), what is the scale factor of this dilation?
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Triangle ABC has vertices A (20, 20), B (15, 10), and C (5, 15). Triangle A'B'C' has vertices A' (4,4), B' (3, 2), and C' (1, 3). What is the scale factor of this dilation?
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Square ABCD was dilated by a scale factor of 7 to create square A'B'C'D' with vertices (21, 7), (49, 35), (56, 42), and (28, 14). What was the original x-coordinate of B' (B)?
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Point A (-2, 14) was dilated by a scale factor of 9 to create Point A'. What is the x-value that corresponds to A'?
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Point A (-2, 14) was dilated by a scale factor of 9 to create Point A'. What is the y-value that corresponds to A'?
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If A (4, -12) was dilated by a scale factor of 1/2, what is the new y-coordinate of A'?
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An equilateral triangle, A, with a side length of 50 was dilated by a scale factor of 1/4. What is the length of triangle A'?
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What is the scale factor in the algebraic representation (x,y) --> (0.4x, 0.4y)?
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Figure A' has a side length of 9 and was dilated by a scale factor of 1/2. What is the side length of Figure A, the pre-image?
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A graph has a y-intercept at -2.5, and the points on the line are dilated by a scale factor of 4. What is the new y-intercept of Line A'?
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Point A (0,4) is dilated by a scale factor of 5 to create Point A'. What is the new y-coordinate of Point A'?
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When a shape is dilated by a scale factor greater than 1, the image is an __________.
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When a shape is dilated by a scale factor less than 1, the image is a __________.
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The transformation that makes a shape bigger or smaller is called a __________.
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When two figures are the same shape and size, they are __________.
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When two figures are the same shape but a different size, they are __________.
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Study Notes
Dilation Scale Factors
- Scale factor determines how much a figure is resized during a dilation.
- A scale factor greater than 1 indicates an enlargement, while less than 1 indicates a reduction.
- When the scale factor is exactly 1, the pre-image and image are congruent.
Calculating Scale Factors
- The scale factor can be calculated by comparing corresponding lengths of sides or coordinates.
- Example: For point A (0,3) and A' (0,33), the scale factor is found to be 11 (33/3).
- Triangle sides can also reveal scale factors – Triangle A with sides 3, 4, 5 dilated to sides 12, 16, 20 has a scale factor of 4.
Algebraic Representation
- Dilation can be expressed algebraically as (kx, ky), where k is the scale factor.
- Example: (2/3x, 2/3y) indicates a scale factor of 2/3.
- Common scale factors: (2.5x, 2.5y) corresponds to a scale factor of 5/2.
Dilation of Points and Shapes
- Dilation of a point A (x,y) by a scale factor k results in point A' (kx, ky).
- Example: Point A (-2, 14) dilated by 9 yields A' (-18, 126).
- Shapes like squares and triangles will have their perimeters and side lengths scaled proportionally.
Dilation Examples
- A square with a perimeter of 4 inches dilated by a scale factor of 2 results in a new perimeter of 8 inches.
- A triangle with vertex (4,5) dilated to (12,15) reflects a scale factor of 3.
- If a figure has a side length of 9 and is dilated by 1/2, the original length can be calculated as 18.
Special Cases
- When shapes have the same shape but different sizes, they are classified as similar; if they are the same shape and size, they are congruent.
Summary of Terms
- Enlargement: Occurs with a scale factor > 1.
- Reduction: Occurs with a scale factor < 1.
- Dilation: The transformation affecting size while maintaining shape.
- Congruent Figures: Figures with the same shape and size.
- Similar Figures: Figures with the same shape but different sizes.
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Description
Test your knowledge on dilations with this quiz! You will calculate scale factors based on provided coordinates, side lengths, and line segments. Perfect for students reviewing geometry concepts.
