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Graph a triangle (LMN) and reflect it over the line y=x to create triangle L'M'N'. Describe the transformation using words. Draw a line segment from point L to the reflecting line, and then draw a line segment from point L' to the reflecting line. What do you notice about the two line segments you drew? Do you think you would see the same characteristic if you drew the line segment connecting M with the reflecting line and then M' with the reflecting line? How do you know?

a) Translation
b) Rotation
c) Reflection
d) Dilation

User Okrunner
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Final answer:

To graph and reflect triangle LMN over the line y=x to obtain L'M'N', the transformation is a reflection. Line segments connecting corresponding points to the line of reflection are congruent and perpendicular, indicating the coordinates (x, y) transform to (y, x). Thus, corresponding points and line segments exhibit the properties of a typical reflection in geometry.

Step-by-step explanation:

To graph triangle LMN and reflect it over the line y=x to create triangle L'M'N', you would use the concept of reflection in geometry. A reflection is a type of transformation where each point of the original figure, in this case triangle LMN, is 'flipped' over a line, known as the line of reflection, to create a mirror image that is the reflected figure, L'M'N'. When you draw a line segment from point L to the reflecting line and then from point L' to the reflecting line, you will notice that these two line segments are congruent and perpendicular to the line of reflection. This is consistent with the properties of reflections over the line y=x, as every point and its image are equidistant from the line of reflection. The same characteristic would be observed if you were to connect points M and M', and N and N', to the reflecting line y=x. This is because, in a reflection over the line y=x, the coordinates of the original points (x, y) become (y, x) for their images. Hence, the transformation undergone by triangle LMN to create triangle L'M'N' is a reflection, not a translation, rotation, or dilation.

User Ajmajmajma
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