Questions and Answers
What is the scale factor of the dilation of Triangle ABC and what are the coordinates of point C?
The scale factor is 1.2 and the coordinates of point C are (-3.6, 3.6).
The dilation has a scale factor between zero and one and is a reduction.
True
What is the scale factor in the dilation if the coordinates of point A are (-7, 6) and the coordinates of point B are (-4, 3)?
1/3
What is the scale factor of the dilation for the quadrilateral with coordinates of D at (36, -12)?
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Which statements are true about the image of a triangle after it has been dilated with a center at the origin?
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What is the scale factor of the triangle with vertices at A(20, -30), B(10, -15), and C(5, -20) if the image of point B has coordinates (2, -3)?
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What are the coordinates of the pre-image of point A under a dilation with a scale factor of 2/1?
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The dilation is an enlargement with a scale factor greater than 1.
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Study Notes
Dilation Concepts
- Dilation involves scaling a geometric figure from a center point, often the origin, in the coordinate plane.
- The scale factor determines the size change; factors greater than 1 indicate enlargement, while factors between 0 and 1 indicate reduction.
Key Example Coordinates and Scale Factors
- Triangle ABC dilated with center at origin results in point C (7.2, 3.6).
- Scale factor: 1.2
- Coordinates of point A: (-3.6, 3.6).
- For a quadrilateral with vertices A(4, -4), B(4, -16), C(12, -16), D(12, -4), if point D dilates to (36, -12):
- Scale factor: 3.
Dilation Outcomes
- If a dilation has a pre-image point A with coordinates (-18, 9) leading to an image with vertices (-12, 6) and (6, -18):
- Scale factor: 2/3.
- Coordinates of point B: (9, -27).
Specific Examples of Scale Factors
- A triangle with vertices A(20, -30), B(10, -15), C(5, -20) dilated to B(2, -3):
- Scale factor: 1/5.
- When the dilation scale factor is 2/1, pre-image coordinates for point A result in (-8, -12).
Characteristics of Dilation
- Dilation with scale factor less than 1 results in a reduction.
- Dilation with scale factor greater than 1 results in an enlargement.
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Description
This quiz consists of flashcards focusing on the concept of dilations in the coordinate plane. You'll explore scale factors, coordinates, and properties of dilation transformations. Test your understanding of these geometric concepts through various scenarios.
