What composition transformation rule has ALMN, L (1,1), M (7,2), and N (5, 7) map onto AL" M" N" L" (2, -1), M" (-4,0), and N" (-2, 5)? (1 point)

Question

• a rotation of 270 degrees clockwise and a move right by 3 and up by 2
• a reflection across the x-axis and a move to the left by 3 and down by 2
• a reflection across the y-axis and a move to the left by 5 and up by 3
© a reflection across the y-axis and a move to the right by 3 and down by 2

Answer 1

To determine the correct composition transformation rule that maps the points of triangle ALMN to the points of triangle AL''M''N'', we need to analyze the positions of the points before and after the transformation.

1. Original Points:

   • L(1, 1)
   • M(7, 2)
   • N(5, 7)

2. Transformed Points:

   • L''(2, -1)
   • M''(-4, 0)
   • N''(-2, 5)

Next, we can check how each point transforms to see which transformation rule fits best.

Step 1: Determine the transformations.

For Point L:

• Original L: (1, 1)
• New L''': (2, -1)

Calculating the transformation from L to L'':

• Change in x = 2 - 1 = 1 (move right by 1)
• Change in y = -1 - 1 = -2 (move down by 2)

For Point M:

• Original M: (7, 2)
• New M''': (-4, 0)

Calculating the transformation from M to M'':

• Change in x = -4 - 7 = -11 (move left by 11)
• Change in y = 0 - 2 = -2 (move down by 2)

For Point N:

• Original N: (5, 7)
• New N''': (-2, 5)

Calculating the transformation from N to N'':

• Change in x = -2 - 5 = -7 (move left by 7)
• Change in y = 5 - 7 = -2 (move down by 2)

Analyzing the Results:

It seems there is a clear movement down by 2 for all points. The x-translations are not consistent across the points, which indicates that there might still be a reflection involved.

Step 2: Check Reflection Across the Y-Axis

Let's analyze:

Reflecting across the y-axis would change the signs of x-coordinates:

• L(1, 1) to L'(-1, 1)
• M(7, 2) to M'(-7, 2)
• N(5, 7) to N'(-5, 7)

None of the transformed points directly correlate with this reflection, meaning the reflection may not entirely capture the transformation we see.

Conclusion

Given that we have a consistent downwards shift of 2 for y-coordinates across all transformations, we need to leverage this with the fact that all x-coordinates saw a shift to the left and then possibly a subsequent transformation of another type as well.

From the options presented, "a reflection across the y-axis and a move to the right by 3 and down by 2" seems the closest possibility, especially since the shifts in x-coordinates seem more erratic, likely indicating a reflection had occurred first that transformed the points before the movement occurred.

Therefore, the correct option is:

• a reflection across the y-axis and a move to the right by 3 and down by 2.