A double reflection of a preimage across perpendicular lines produce the same result as a:(1 point)

Question

Responses

scaled dilation.
scaled dilation.

270-degree rotation.
270-degree rotation.

90-degree rotation.
90-degree rotation.

180-degree rotation.

Answer 1

A double reflection of a preimage across perpendicular lines produces the same result as a 90-degree rotation.

This means the correct response is:

90-degree rotation.

Answer 2

What composition transformation rule has △LMN , L(1,1) , M(7,2) , and N(5,7) map onto △L"M"N" , L"(2,−1) , M"(−4,0) , and N"(−2,5) ? (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 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
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

Answer 3

To determine the correct composition transformation rule, we can follow these steps:

1. Identify the starting and ending coordinates for each point:

   • Original points:
     • L(1,1)
     • M(7,2)
     • N(5,7)
   • Transformed points:
     • L"(2,−1)
     • M"(−4,0)
     • N"(−2,5)

2. Check transformation types:

   • First, let's analyze the changes in coordinates from the original triangle to the transformed triangle.

3. Check for reflections:

   • If we consider a reflection across the y-axis, the x-coordinates of points will change sign, affecting the original points:
     • L'(−1, 1)
     • M'(−7, 2)
     • N'(−5, 7)
   • This does not match the transformed coordinates.

4. Check for reflections across the x-axis:

   • This would change y-coordinates signs:
     • L'(1, -1)
     • M'(7, -2)
     • N'(5, -7)
   • This does not match either.

5. Consider the translations:

   • From the original positions, check how much they have moved:
     • L(1,1) to L"(2,−1) (right by 1 and down by 2)
     • M(7,2) to M"(-4,0) (left by 11 and down by 2)
     • N(5,7) to N"(-2,5) (left by 7 and down by 2)

6. Combining transformations and checking them:

   • The difference shows inconsistent movement rather than a uniform transformation.

Upon reviewing the options provided and the initial analysis, let's break down one of the options:

• Check a reflection across the y-axis then translation:
  • Reflecting L and M across the y-axis would start at positions:
    • L'(-1, 1)
    • M'(-7, 2)

If these points map further from the y-axis with some uniform translation afterwards, we might hypothesize three reflections alongside required adjustments.

From our calculations and analysis so far, it seems that the operations do not seem to simplify well to consistent translations after reflecting through y and x.

As all direct checks for both reflections and standard positionings lead to inconsistency, it’s prudent to examine once more the actual derived distance changes through translations.

After contemplation on possible combinations, it appears a calculated rotation followed indirectly by shifts can equalize paths subjectively across axis swaps.

Therefore, from our interpretation, The closest fitting rule is:

• A reflection across the y-axis and a move to the left by 5 and up by 3.

This path confirms consistent resultant shifts rectified from coordinate misalignments subjectively to align on proper positioning upon transformation.