Question

Triangle NMO is drawn with vertices N(−5, 2), M(−2, 1), O(−3 , 3). Determine the image vertices of N′M′O′ if the preimage is reflected over x = −3.
N′(5, 2), M′(2, 1), O′(3, 3)
N′(−1, 2), M′(−4, 1), O′(−3, 3)
N′(1, 2), M′(−2, 1), O′(−1, 3)
N′(−5, −2), M′(−2, −1), O′(−3, −3)

Answer 1

To find the image vertices of triangle NMO when reflected over the line \( x = -3 \), we first need to understand how to reflect each point about this line.

The x-coordinate of any point reflected over the line \( x = -3 \) can be determined using the formula:
\[
x' = -3 - (x + 3) = -3 - x - 3 = -6 - x
\]

We now apply this to each vertex of the triangle:

1. For vertex \( N(-5, 2) \):
\[
x' = -6 - (-5) = -6 + 5 = -1
\]
So, \( N'(-1, 2) \).

2. For vertex \( M(-2, 1) \):
\[
x' = -6 - (-2) = -6 + 2 = -4
\]
So, \( M'(-4, 1) \).

3. For vertex \( O(-3, 3) \):
\[
x' = -6 - (-3) = -6 + 3 = -3
\]
So, \( O'(-3, 3) \).

Combining these results, we have the reflected vertices:
- \( N'(-1, 2) \)
- \( M'(-4, 1) \)
- \( O'(-3, 3) \)

Thus, the image vertices of triangle NMO after reflection over \( x = -3 \) are:
\[
N'(-1, 2), M'(-4, 1), O'(-3, 3)
\]

This matches the answer:
\[
N′(−1, 2), M′(−4, 1), O′(−3, 3)
\]