What composition transformation rule has applied to have △LMN map onto ​△L′M′N′ , if the coordinates are: ​​​​ L(8,3) , M(4,6) , and N(5,9) L′(−10,−3) , M′(−6,0) , and N′(−7,3) ? (1 point) Responses a reflection across the x-axis and a move to the right by 2 and down by 6 a reflection across the x-axis and a move to the right by 2 and down by 6 a reflection over the y-axis and a move to the left by 6 and down by 2 a reflection over the y-axis and a move to the left by 6 and down by 2 a reflection over the y-axis and a move to the left by 2 and down by 6 a reflection over the y-axis and a move to the left by 2 and down by 6 a rotation of 270 degrees clockwise and a move right by 2 and up by 6 a rotation of 270 degrees clockwise and a move right by 2 and up by 6 Skip to navigation

Answer 1

To determine the transformation that maps triangle \( \triangle LMN \) to triangle \( \triangle L'M'N' \), we can analyze the coordinates:

• \( L(8, 3) \) maps to \( L'(-10, -3) \)
• \( M(4, 6) \) maps to \( M'(-6, 0) \)
• \( N(5, 9) \) maps to \( N'(-7, 3) \)

Step 1: Identify the type of transformation.

1. Calculate the change in coordinates for point L: \[ L \to L': \quad (8, 3) \to (-10, -3) \] Change in x: \( -10 - 8 = -18 \)

   Change in y: \( -3 - 3 = -6 \)

   So \( L \) moves left by 18 units and down by 6 units.

2. Calculate the change in coordinates for point M: \[ M \to M': \quad (4, 6) \to (-6, 0) \] Change in x: \( -6 - 4 = -10 \)

   Change in y: \( 0 - 6 = -6 \)

   So \( M \) moves left by 10 units and down by 6 units.

3. Calculate the change in coordinates for point N: \[ N \to N': \quad (5, 9) \to (-7, 3) \] Change in x: \( -7 - 5 = -12 \)

   Change in y: \( 3 - 9 = -6 \)

   So \( N \) moves left by 12 units and down by 6 units.

Step 2: Consistency of Movements

All points appear to be translated downwards by 6 units. However, the x-coordinates of L, M, and N show different movements left (-18, -10, -12), indicating a possible reflection over the y-axis as well.

Step 3: Checking for Reflection Over y-axis

After reflecting over the y-axis, the new coordinates would be calculated as:

• The reflection of \( L(8, 3) = (-8, 3) \)
• The reflection of \( M(4, 6) = (-4, 6) \)
• The reflection of \( N(5, 9) = (-5, 9) \)

Then, after moving to the left and down as noted earlier, we need to apply further translations.

• After reflecting \( L(-8, 3) \) and then translating left by 2 and down by 6: \[ (-8-2, 3-6) = (-10, -3) \quad \text{(which matches } L') \]
• After reflecting \( M(-4, 6) \): \[ (-4-2, 6-6) = (-6, 0) \quad \text{(which matches } M') \]
• After reflecting \( N(-5, 9) \): \[ (-5-2, 9-6) = (-7, 3) \quad \text{(which matches } N') \]

Conclusion:

The transformation that maps \( \triangle LMN \) to \( \triangle L'M'N' \) is:

• A reflection over the y-axis and a move to the left by 2 and down by 6.

The correct option is: a reflection over the y-axis and a move to the left by 2 and down by 6.