what composition transformation rule has triangle LMN, L(1, 1), M(7, 2) and N(5, 7) map onto. triangle L’’M’’N’’, L’’ (2, -1), (-4, 0), and N’’ (-2, 5)?
A. A reflection across the Y axis and a move to the right by 3 and down by 2.
B. A reflection across the X axis in the move to the left by 3 and down by 2.
C. A rotation of 270° clockwise and a move right by 3 and up by 2.
D. A reflection across the Y axis and a move to the left by 5 and up by 3.
To determine the composition transformation, we need to compare the coordinates of the original triangle LMN with the coordinates of the transformed triangle L''M''N''.
Let's start by analyzing the X-coordinates:
- L(1, 1) corresponds to L''(2, -1): The X-coordinate increased by 1.
- M(7, 2) corresponds to M''(-4, 0): The X-coordinate decreased by 11.
- N(5, 7) corresponds to N''(-2, 5): The X-coordinate decreased by 7.
Next, let's analyze the Y-coordinates:
- L(1, 1) corresponds to L''(2, -1): The Y-coordinate decreased by 2.
- M(7, 2) corresponds to M''(-4, 0): The Y-coordinate decreased by 2.
- N(5, 7) corresponds to N''(-2, 5): The Y-coordinate decreased by 2.
Based on these comparisons, we can conclude that the composition transformation consists of a move to the left by 3 and down by 2 (or simply a move to the left by 3 and up by -2).
Therefore, the correct answer is:
B. A reflection across the X axis in the move to the left by 3 and down by 2.