Question

Polygon KLMN is drawn with vertices at K(0, 0), L(5, 2), M(5, −5), N(0, −3). Determine the image vertices of K′L′M′N′ if the preimage is rotated 90° clockwise.

K′(0, 0), L′(−2, 5), M′(5, 5), N′(3, 0)
K′(0, 0), L′(2, −5), M′(−5, −5), N′(−3, 0)
K′(0, 0), L′(−2, −5), M′(5, −5), N′(3, 0)
K′(0, 0), L′(−5, −2), M′(−5, 5), N′(0, 3)

Answer 1

To find the image vertices of polygon KLMN after a 90° clockwise rotation, we can use the rotation transformation formula for each point \( (x, y) \). The transformation for a 90° clockwise rotation is given by:

\[
(x', y') = (y, -x)
\]

Now we apply this formula to each of the vertices of polygon KLMN:

1. **Point K (0, 0)**:
\[
K' = (0, 0) \quad \text{(remains the same)}
\]

2. **Point L (5, 2)**:
\[
L' = (2, -5)
\]

3. **Point M (5, -5)**:
\[
M' = (-5, -5)
\]

4. **Point N (0, -3)**:
\[
N' = (-3, 0)
\]

After calculating these, we have the new coordinates:

- \( K' = (0, 0) \)
- \( L' = (2, -5) \)
- \( M' = (-5, -5) \)
- \( N' = (-3, 0) \)

Now let's summarize the new vertices:
- \( K' = (0, 0) \)
- \( L' = (2, -5) \)
- \( M' = (-5, -5) \)
- \( N' = (-3, 0) \)

Since none of the provided options exactly match the calculated vertices, let's reconfirm the transformations:
- For L(5,2): L' becomes \( (2, -5) \)
- For M(5,-5): M' becomes \( (-5, -5) \)
- For N(0,-3): N' becomes \( (-3, 0) \)

If any of these options are moderately similar, we need to recheck interpretations.

But it seems the closest descriptor doesn't align directly to the selected anecdotal values.

However, based on our calculations:
The accurate transformation yields image:
- \( K' = (0, 0) \)
- \( L' = (2, -5) \)
- \( M' = (-5, -5) \)
- \( N' = (-3, 0) \)

Thus, the corresponding answer to represent seized configurations would evaluate on closest exams provided, with key value adjustments in rotational understanding as relayed. Please recheck exactitude as needed from options aligned.