The transformation rule provided is T1, -4 CompositionRO, 180°(x, y). This rule combines two operations:

1. Translation (T1, -4): This means the rectangle is translated (shifted) 1 unit to the right and 4 units down.
2. Rotation (RO, 180°): This means the rectangle is rotated by 180 degrees around the origin (0, 0), which effectively flips it both horizontally and vertically.

Step 1: Apply the Translation (T1, -4)

The original rectangle KLMN has vertices at:

• $K(3, -4)$
• $L(3, -1)$
• $M(5, -1)$
• $N(5, -4)$

Applying the translation $T(1, -4)$, we add 1 to the x-coordinates and subtract 4 from the y-coordinates:

• New $K(3+1, -4-4) = (4, -8)$
• New $L(3+1, -1-4) = (4, -5)$
• New $M(5+1, -1-4) = (6, -5)$
• New $N(5+1, -4-4) = (6, -8)$

So, after the translation, the new vertices are: $(4, -8)$, $(4, -5)$, $(6, -5)$, and $(6, -8)$.

Step 2: Apply the 180° Rotation

The 180° rotation around the origin transforms the point $(x, y)$ into $(-x, -y)$. Applying this to each of the translated points:

• Rotate $(4, -8)$ to $(-4, 8)$
• Rotate $(4, -5)$ to $(-4, 5)$
• Rotate $(6, -5)$ to $(-6, 5)$
• Rotate $(6, -8)$ to $(-6, 8)$

So, the final vertices after the 180° rotation are $(-4, 8)$, $(-4, 5)$, $(-6, 5)$, and $(-6, 8)$.

Step 3: Compare with Given Rectangles

Now, we compare these final coordinates with the given rectangles:

• Rectangle 1 has vertices at $(-4, 6), (-4, 4), (-1, 4), (-1, 6)$. This does not match.
• Rectangle 2 has vertices at $(0, 0), (-2, 0), (-2, 3), (0, 3)$. This does not match.
• Rectangle 3 has vertices at $(-2, 0), (-4, 0), (-2, -3), (-4, -3)$. This does not match.
• Rectangle 4 has vertices at $(1, 0), (4, 0), (1, 2), (4, 2)$. This does not match either.

Since none of the given rectangles match the final transformed coordinates $(-4, 8), (-4, 5), (-6, 5), (-6, 8)$, it appears there may be a misunderstanding or discrepancy in the problem description or a mislabeling of the options. However, based on the transformation procedure, the correct final image should be found by visually matching this shape with the options provided.

Would you like to proceed with further clarifications or corrections?

Related Questions:

1. What does a 180° rotation do to a shape's orientation on a coordinate plane?
2. How does translating a figure affect its coordinates?
3. What are the steps to solve problems involving composite transformations?
4. How do you apply a combination of translation and rotation to a polygon on the coordinate plane?
5. How would you verify your transformation results if multiple options are given?

Tip: When working with composite transformations, break them down step by step and check each intermediate result.