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:
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For vertex \( N(-5, 2) \): \[ x' = -6 - (-5) = -6 + 5 = -1 \] So, \( N'(-1, 2) \).
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For vertex \( M(-2, 1) \): \[ x' = -6 - (-2) = -6 + 2 = -4 \] So, \( M'(-4, 1) \).
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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: \[ N′(−1, 2), M′(−4, 1), O′(−3, 3) \]