Graph a triangle (LMN) and rotate it 180° around the origin to create triangle L′M′N′. Describe the transformation using words. Make sure you refer to the characteristics and the coordinates.
Draw a line through points L and L′ and through M and M′. What do you notice about the lines you drew? Do you think you would notice the same characteristics if you drew another line through points N and N′? How do you know?

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  a) the transformation is a reflection across the origin; both coordinates are negated

  b) the lines joining a point with its image go through the origin

  c) yes; the lines joining a point with its image go through the origin

Step-by-step explanation:

a) Rotation 180° about the origin negates both coordinates. It is equivalent to a reflection across both axes, or a reflection across the origin.

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b) The lines LL' and MM' both go through the origin.

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c) All lines joining a point and its image will go through the point of reflection, whatever it might be. Here, the point of reflection is the origin, so any line joining a point (N) and its image (N') will go through the origin.

the correct answer is 828.07