To move triangle ABC to triangle EGH and show that the triangles are congruent, we can follow these steps:
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Reflection over the x-axis:
- Reflect triangle ABC across the x-axis. This will transform the vertices of triangle ABC from their original positions:
- A(-6, -2) → A'(-6, 2)
- B(-4, -5) → B'(-4, 5)
- C(-1, -5) → C'(-1, 5)
- Reflect triangle ABC across the x-axis. This will transform the vertices of triangle ABC from their original positions:
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Translation:
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After reflecting triangle ABC, we need to translate the new triangle A'B'C' to match triangle EGH. The vertices of triangle EGH are:
- E(4, 6)
- G(7, 6)
- H(2, 3)
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The reflected and translated positions should ideally match the positions of triangle EGH.
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We can find the translation by determining the difference between corresponding points. Taking the point A'(-6, 2) and wanting it to go to E(4, 6):
- To move from -6 to 4 on the x-axis: \( 4 - (-6) = 10 \)
- To move from 2 to 6 on the y-axis: \( 6 - 2 = 4 \)
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Thus, the translation needed is (10, 4).
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Putting this together, the sequence of transformations needed to move triangle ABC to triangle EGH is: Reflection over the x-axis, then a translation of (10, 4).