To determine the transformation that maps triangle \( \triangle LMN \) with vertices \( L(1,1) \), \( M(7,2) \), and \( N(5,7) \) to triangle \( \triangle L"M"N" \) with vertices \( L"(2,-1) \), \( M"(-4,0) \), and \( N"(-2,5) \), we can analyze the movements of the vertices.
-
Identify the original and transformed points:
- \( L(1, 1) \) to \( L"(2, -1) \)
- \( M(7, 2) \) to \( M"(-4, 0) \)
- \( N(5, 7) \) to \( N"(-2, 5) \)
-
Determine the transformations:
-
For vertex \( L(1, 1) \) to \( L"(2, -1) \):
- Move right by \( 2 - 1 = 1 \) (increase in x-coordinate)
- Move down by \( -1 - 1 = -2 \) (decrease in y-coordinate)
-
For vertex \( M(7, 2) \) to \( M"(-4, 0) \):
- Move left by \( -4 - 7 = -11 \) (decrease in x-coordinate)
- Move down by \( 0 - 2 = -2 \) (decrease in y-coordinate)
-
For vertex \( N(5, 7) \) to \( N"(-2, 5) \):
- Move left by \( -2 - 5 = -7 \) (decrease in x-coordinate)
- Move down by \( 5 - 7 = -2 \) (decrease in y-coordinate)
-
The changes in orientation imply that a reflection might be taking place.
-
Test for reflections across axes:
- The transformation: reflect across the y-axis and then translate could possibly yield the movement observed in the vertices:
- Reflect \( L(1, 1) \) across y-axis: Moves to \( (-1, 1) \) then translating right by 3 and down by 2 results in \( (2, -1) \).
- Reflect \( M(7, 2) \) across y-axis: Moves to \( (-7, 2) \) then translating right by 3 gives \( (-4, 0) \).
- Reflect \( N(5, 7) \) across the y-axis: Moves to \( (-5, 7) \) then translating right by 3 gives \( (-2, 5) \).
- The transformation: reflect across the y-axis and then translate could possibly yield the movement observed in the vertices:
-
Select the correct transformation: Based on these calculations, the correct transformation rule is:
A reflection across the y-axis and a move to the right by 3 and down by 2.
1 answer