Question

Triangle NMO is drawn with vertices N(−4, −2), M(−1, −1), O(−4 , −5). Determine the image coordinates of N′M′O′ if the preimage is translated 5 units to the left.

N′(1, −2), M′(4, −1), O′(1, −5)
N′(−4, 3), M′(−1, 4), O′(−4, 0)
N′(−9, −2), M′(−6, −1), O′(−9, −5)
N′(−4, −7), M′(−1, −6), O′ (−4, −10)

Answer 1

To determine the image coordinates \( N'M'O' \) after translating the triangle \( NMO \) 5 units to the left, we must subtract 5 from the x-coordinates of each vertex.

The original coordinates of the vertices are:
- \( N(-4, -2) \)
- \( M(-1, -1) \)
- \( O(-4, -5) \)

Now we will calculate the new coordinates after the translation:

1. For point \( N \):
\[
N' = (-4 - 5, -2) = (-9, -2)
\]

2. For point \( M \):
\[
M' = (-1 - 5, -1) = (-6, -1)
\]

3. For point \( O \):
\[
O' = (-4 - 5, -5) = (-9, -5)
\]

Now we have the new coordinates:
- \( N'(-9, -2) \)
- \( M'(-6, -1) \)
- \( O'(-9, -5) \)

However, it seems there's a mistake in the calculation for \( M' \). Let's correct M':

The correct new coordinates after translation should be:
- \( N'(-9, -2) \)
- \( M'(-6, -1) \)
- \( O'(-9, -5) \)

None of the provided options exactly match our calculations for the transformed coordinates; however, the correct answer based on shifting each coordinate 5 units to the left would be:

- \( N'(-9, -2) \)
- \( M'(-6, -1) \)
- \( O'(-9, -5) \)

Unfortunately, **none of the answer choices provided** matches this result.

Please double-check your question for any discrepancies or clarifications regarding the translation.