To determine the coordinates of the vertices of trapezoid EFGH after a dilation with a scale factor of 3 about the origin, we can apply the dilation transformation to each vertex. The formula for dilating a point \((x, y)\) by a scale factor \(k\) about the origin is given by:
\[ (x', y') = (kx, ky) \]
Using this formula, let's calculate the new coordinates for each vertex:
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For vertex E (1, 1): \[ E' = (3 \times 1, 3 \times 1) = (3, 3) \]
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For vertex F (3, 1): \[ F' = (3 \times 3, 3 \times 1) = (9, 3) \]
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For vertex G (4, -2): \[ G' = (3 \times 4, 3 \times -2) = (12, -6) \]
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For vertex H (0, -2): \[ H' = (3 \times 0, 3 \times -2) = (0, -6) \]
Now, summarizing the coordinates of the vertices of the dilated trapezoid E'F'G'H':
- \(E'\) is (3, 3)
- \(F'\) is (9, 3)
- \(G'\) is (12, -6)
- \(H'\) is (0, -6)
Now, let's evaluate the given statements:
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The coordinates of E' are (1, 3).
- False; the coordinates of \(E'\) are (3, 3).
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The coordinates of G' are (7, 1).
- False; the coordinates of \(G'\) are (12, -6).
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The coordinates of H' are (0, -6).
- True; the coordinates of \(H'\) are correct.
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Vertex F' is located in Quadrant I.
- True; \(F' (9, 3)\) is located in Quadrant I.
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Vertex G' is located in Quadrant II.
- False; \(G' (12, -6)\) is located in Quadrant IV.
Based on this analysis, the two true statements are:
- The coordinates of H' are (0, -6).
- Vertex F' is located in Quadrant I.