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

O 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
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

Answer 1

To determine which transformation maps points L, M, and N to L", M", and N", we can analyze the given coordinates:

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, let’s break down the transformations that might occur between the original points and the transformed points.

Analyzing Each Transformation Option:

1. Reflection across the y-axis and a move to the left by 5 and up by 3:

   • Reflect across the y-axis:
     • L (1, 1) → L' (-1, 1)
     • M (7, 2) → M' (-7, 2)
     • N (5, 7) → N' (-5, 7)
   • Move left by 5 (subtract 5 from x) and up by 3 (add 3 to y):
     • L' → L'' (-1 - 5, 1 + 3) = (-6, 4)
     • M' → M'' (-7 - 5, 2 + 3) = (-12, 5)
     • N' → N'' (-5 - 5, 7 + 3) = (-10, 10)
   • This does not match the transformed points.

2. Reflection across the y-axis and a move to the right by 3 and down by 2:

   • Same reflection gives:
     • L' (-1, 1)
     • M' (-7, 2)
     • N' (-5, 7)
   • Move right by 3 (add 3 to x) and down by 2 (subtract 2 from y):
     • L' → L'' (-1 + 3, 1 - 2) = (2, -1)
     • M' → M'' (-7 + 3, 2 - 2) = (-4, 0)
     • N' → N'' (-5 + 3, 7 - 2) = (-2, 5)
   • This matches the transformed points L", M", N".

3. Rotation of 270 degrees clockwise and a move right by 3 and up by 2:

   • A 270-degree rotation (or -90-degree rotation):
     • L (1, 1) → L' (1, -1)
     • M (7, 2) → M' (2, -7)
     • N (5, 7) → N' (7, -5)
   • Then apply the move:
     • L' → L'' (1 + 3, -1 + 2) = (4, 1)
     • M' → M'' (2 + 3, -7 + 2) = (5, -5)
     • N' → N'' (7 + 3, -5 + 2) = (10, -3)
   • This does not match the transformed points.

4. Reflection across the x-axis and a move to the left by 3 and down by 2:

   • Reflect across the x-axis:
     • L (1, 1) → L' (1, -1)
     • M (7, 2) → M' (7, -2)
     • N (5, 7) → N' (5, -7)
   • Move left by 3 and down by 2:
     • L' → L'' (1 - 3, -1 - 2) = (-2, -3)
     • M' → M'' (7 - 3, -2 - 2) = (4, -4)
     • N' → N'' (5 - 3, -7 - 2) = (2, -9)
   • This does not match the transformed points.

Conclusion:

The transformation that maps points L, M, N onto L", M", and N" is the reflection across the y-axis and a move to the right by 3 and down by 2.

The answer is: a reflection across the y-axis and a move to the right by 3 and down by 2.