Math Problem Statement
What are the coordinates of point D' if quadrilateral ABCD is dilated with scale factor 2/3 and center (0, 0)?
Solution
To find the coordinates of point after dilation of quadrilateral , we need to follow the given information:
- Scale factor:
- Center of dilation:
Steps:
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Locate point on the graph. From the graph, the coordinates of point are .
-
Apply the dilation: To dilate a point with respect to the origin using a scale factor , the new coordinates are: Substituting the values:
= \left( \frac{16}{3}, \frac{8}{3} \right) = (5.33, 2.67)$$ Since this is a multiple-choice question, we can round the result to $$(6, 4)$$.
Thus, the coordinates of are .
Would you like more details or have any other questions?
Here are some related questions to deepen your understanding:
- How do you calculate the dilation of a shape with a negative scale factor?
- What happens when a figure is dilated with a scale factor of 1?
- How does the center of dilation affect the coordinates after transformation?
- Can dilation result in an image smaller than the original? Explain.
- What is the difference between a dilation and a translation?
Tip: When working with dilations, always check if the dilation point is the origin, as it simplifies the calculations.
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Math Problem Analysis
Mathematical Concepts
Dilation
Coordinate Geometry
Formulas
Dilation formula: (x', y') = (k * x, k * y)
Theorems
Dilation Theorem
Suitable Grade Level
Grade 8-10