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

Question

A. A rotation of 270 degrees clockwise and move right by 3 and up by 2
B. a reflection across the y-axis and a move to the right by 3 and down by two
C. a reflection across the y-axis and a move to the left by 5 and up by 3
D. A reflection across the x-axis and a move to the left by 3 and down by 2

Answer 1

To determine the composition transformation rule that maps triangle LMN to triangle L''M''N'', we need to analyze the coordinates of the points.

The original triangle has vertices:

• L(1, 1)
• M(7, 2)
• N(5, 7)

The transformed triangle has vertices:

• L''(2, 1)
• M''(-4, 0)
• N''(-2, 5)

Let's first look for any transformations one by one.

1. Check for a reflection:

   • A reflection across the y-axis would change the x-coordinates from positive to negative. So let's reflect the points across the y-axis:
     • L(1, 1) → L'(−1, 1)
     • M(7, 2) → M'(−7, 2)
     • N(5, 7) → N'(−5, 7)

   This does not give us the new points, so we can eliminate the reflection across the y-axis.

   Now let's try a reflection across the x-axis:

   • L(1, 1) → L'(1, -1)
   • M(7, 2) → M'(7, -2)
   • N(5, 7) → N'(5, -7)

   This also does not match.

2. Try moving the points: Let's just change the positions directly as provided in the options.

   According to option A, a rotation of 270 degrees clockwise means:

   • For point L(1, 1), rotating gives us:
     • (1,1) → (1,-1) → (−1,−1)
   • Next, move right by 3 and up by 2 gives:
     • (−1,−1) → (−1+3,−1+2) → (2,1)

   For M and N, applying the same transformation does not yield correct results.

3. If we try B - check for reflection across the y-axis then move: Let's see this for points:

   • After reflecting across the y-axis:
     • L(1,1) → L'(-1, 1)
     • M(7,2) → M'(-7, 2)
     • N(5,7) → N'(-5, 7)

   Now move all three points right by 3 and down by 2:

   • L'(-1 + 3, 1 - 2) = (2, -1)
   • M'(-7 + 3, 2 - 2) = (-4, 0)
   • N'(-5 + 3, 7 - 2) = (-2, 5)

   This partially matches our expected transformed triangle (matches M'' and N'' but not L'').

4. If we try C - reflection across the y-axis and move:

• Reflecting yields: L(-1, 1), M(-7, 2), N(-5, 7)

Then moving left by 5 and up by 3:

• (L' - 5, 1 + 3)
• M'(-7 - 5, 2 + 3) = -12, 5

So none of them exactly give the right ones and we might not have covered other potential matrix involvements that might suit contributions.

So the conclusion may not exactly meet the point we desire explicitly with the options stated due to coordinate mistakes, hence we can settle amongst clear verification ongoing from your straight routes having slight differences though movement specs are straight evident elsewhere giving connection around transformations too.

So technically, none accurately provide perfect fits, but B covered closer connection after and rechecks inline!

Answer: B seems closest to approximate transformation specifics though not accurate mapping systematically.