Question What composition transformation rule has%C2%A0△LMN ,%C2%A0L(1,1) ,%C2%A0M(7,2) , and N(5,7) %C2%A0map onto △L"M"N" ,%C2%A0L"(2,−1) ,%C2%A0M"(−4,0) ,%C2%A0and N"(−2,5) ?%C2%A0(1 point) Responses a rotation of 270 degrees clockwise and a move right by 3 and up by 2 a rotation of 270 degrees clockwise and a move right by 3 and up 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 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 reflection across the y -axis and a move to the right by 3 and down by 2 a reflection across the x-axis and a move to the left by 3 and down by 2

Question

Question What composition transformation rule has%C2%A0△LMN ,%C2%A0L(1,1) ,%C2%A0M(7,2) , and N(5,7) %C2%A0map onto △L"M"N" ,%C2%A0L"(2,−1) ,%C2%A0M"(−4,0) ,%C2%A0and N"(−2,5) ?%C2%A0(1 point) Responses  a rotation of 270 degrees clockwise and a move right by 3 and up by 2 a rotation of 270 degrees clockwise and a move right by 3 and up 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 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 reflection across the y -axis and a move to the right by 3 and down by 2  a reflection across the x-axis and a move to the left by 3 and down by 2

GPT-4o mini · Answer

To determine the transformation that maps triangle \( \triangle LMN \) with vertices \( L(1,1) \), \( M(7,2) \), and \( N(5,7) \) onto triangle \( \triangle L"M"N" \) with vertices \( L"(2,-1) \), \( M"(-4,0) \), and \( N"(-2,5) \), we can analyze the changes to the coordinates of the vertices.

Step 1: Translate Points

Calculate the translations needed for each point from \( L \) to \( L" \), \( M \) to \( M" \), and \( N \) to \( N" \).

For \( L \): \[ L(1, 1) \rightarrow L"(2, -1) \]

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

For \( M \): \[ M(7, 2) \rightarrow M"(-4, 0) \]

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

For \( N \): \[ N(5, 7) \rightarrow N"(-2, 5) \]

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

Step 2: Determine Patterns for Transformation From \( L(1, 1) \) to \( L"(2, -1) \), we have:

Move right by 1 and down by 2.
However, from \( M \) and \( N \), the pattern shows changes in only the \( x \)-coordinates or different magnitudes that do not maintain consistency in a simple translation.

Step 3: Reflection Analysis The transformation appears more complex than a simple translation. A reflection about the y-axis also changes the sign of the x-coordinates while altering the y-coordinates.

Given the transformations resulted in drastic shifts that suggest reflections rather than basic moves, we evaluate their movements.

Final Observations: Since we're seeing:

Reflection across the y-axis indicating changes in the x components specifically
Then observe y values to adjust by some quantities

This reflects that based on the provided options:

The option reflecting across the y-axis then moving yields the most consistent result with the x-component's direction and shifts with transformation combinations.

From our logic and combinations, it's apparent that: The composition transformation that maps \( \triangle LMN \) to \( \triangle L"M"N" \) is likely: A reflection across the y-axis and a move to the left by 5 and up by 3.