In the coordinate plane, △JKL has vertices J(9,–3), K(3,5), and L(5,9), and △MNO has vertices M(–6,–3), N(6,6), and O(12,3).Select the sequence of transformations that can be applied to △JKL to show that it is similar to △MNO.
Question
In the coordinate plane, △JKL has vertices J(9,–3), K(3,5), and L(5,9), and △MNO has vertices M(–6,–3), N(6,6), and O(12,3).Select the sequence of transformations that can be applied to △JKL to show that it is similar to △MNO.
Solution
To show that triangle JKL is similar to triangle MNO, we can apply a sequence of transformations. Here are the steps:
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Translation: We can start by shifting triangle JKL to the left by 6 units. This will align vertex J of triangle JKL with vertex M of triangle MNO.
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Reflection: Next, we can reflect the translated triangle over the y-axis. This will make the triangle face in the same direction as triangle MNO.
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Dilation: Finally, we can dilate the triangle by a factor of 1/2 with respect to the origin. This will make the triangle the same size as triangle MNO.
After these transformations, triangle JKL should be in the same position and have the same size as triangle MNO, showing that they are similar.
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