Math Problem Statement
What is the image of left parenthesis, minus, 8, comma, 8, right parenthesis(−8,8) after a dilation by a scale factor of one quarter 4 1 centered at the origin?
Solution
The point you are working with is , and the scale factor for the dilation is . Since the dilation is centered at the origin, you can apply the scale factor directly to both the - and -coordinates of the point.
Step-by-step process:
- Start with the point .
- Apply the scale factor to each coordinate:
- For the -coordinate:
- For the -coordinate:
Thus, after the dilation, the image of the point is:
Would you like any further details on this process, or do you have any questions?
Here are 5 related questions to consider:
- How do you find the image of a point after dilation with a different center?
- What happens to a point when it is dilated by a factor greater than 1?
- How do you calculate dilations in higher dimensions, such as 3D space?
- How does dilation affect the distance between two points?
- How do you reverse a dilation (find the pre-image of a point)?
Tip: When applying dilations, always remember that the distance from the center of dilation changes by the scale factor, but the direction remains the same.
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Math Problem Analysis
Mathematical Concepts
Dilation
Coordinate Geometry
Transformations
Formulas
Dilation formula: (x', y') = (kx, ky) where k is the scale factor
Theorems
Dilation Theorem
Suitable Grade Level
Grades 8-10