In the coordinate plane, △DEF has vertices D(3,–2), E(5,–3), and F(4,–4), and △GHI has vertices G(5,5), H(–5,0), and I(0,–3).Select the sequence of transformations that can be applied to △DEF to show that it is similar to △GHI.
Question
In the coordinate plane, △DEF has vertices D(3,–2), E(5,–3), and F(4,–4), and △GHI has vertices G(5,5), H(–5,0), and I(0,–3).Select the sequence of transformations that can be applied to △DEF to show that it is similar to △GHI.
Solution
To show that triangle DEF is similar to triangle GHI, we can apply a sequence of transformations. Here are the steps:
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Translation: Move triangle DEF up by 7 units. This changes the coordinates of D, E, and F to D'(3,5), E'(5,4), and F'(4,3) respectively.
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Reflection: Reflect the translated triangle DEF across the y-axis. The new coordinates become D''(-3,5), E''(-5,4), and F''(-4,3).
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Rotation: Rotate the reflected triangle 90 degrees counterclockwise about the origin. The new coordinates are D'''(5,3), E'''(4,-5), and F'''(3,-4).
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Scaling: Scale the rotated triangle by a factor of 5. The final coordinates are D''''(25,15), E''''(20,-25), and F''''(15,-20).
After these transformations, triangle DEF has the same shape as triangle GHI, but it is 5 times larger. Therefore, triangle DEF is similar to triangle GHI.
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