Final answer:
To describe the transformation of triangle LMN rotated 180° around the origin to create L'M'N', we note that the coordinates of the new vertices are the opposites of the original. Lines that connect corresponding vertices (L to L', M to M', and N to N') all pass through the origin and are collinear. This is characteristic of 180° rotations about the origin.
Step-by-step explanation:
To graph triangle LMN and rotate it 180° around the origin to create triangle L'M'N', we follow these steps:
- Plot the original triangle LMN on a coordinate grid with vertices L, M, and N at specific coordinates.
- Apply a 180° rotation around the origin. This means each point of triangle LMN will be moved to a point that is directly opposite to it across the origin. The coordinates of each vertex after the transformation will be the negatives of the original coordinates. For example, if vertex L has coordinates (x, y), then L' will have coordinates (-x, -y).
- The transformed triangle L'M'N' will be congruent to triangle LMN but will be in a different position on the grid.
Describing this transformation in words, we have rotated triangle LMN through 180° about the origin, which results in a congruent triangle L'M'N' that is a mirror image across the origin. The coordinates of the vertices have the same absolute values but opposite signs.
When we draw lines through points L and L' and through M and M', we notice that these lines intersect at the origin and are collinear with it. This is because rotation of 180° places points directly opposite each other with respect to the origin. The same characteristic will be observed if we draw a line through points N and N' - this line too will pass through the origin and N and N' will lie on it.