Question

ASAP i have three other math questions posted as well i give 100 for each and brainlit to the right answers

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 = −2.

N′(5, −2), M′(2, 1), O′(3, 3)
N′(−2, 2), M′(1, 1), O′(0, 3)
N′(1, 2), M′(−2, 1), O′(−1, 3)
N′(−5, −2), M′(−2, −1), O′(−3, −3)

Answer 1

Answer: Option (C): N′(1, 2), M′(−2, 1), O′(−1, 3).

Explanation:

To reflect the preimage over x = -2, we can use the formula for reflecting a point (x, y) over a vertical line x = a:

(x', y) = (2a - x, y)

In this case, the vertical line is x = -2, so a = -2.

So we can find the image vertices as follows:

N' = (2(-2) - (-5), 2) = (4 + 5, 2) = (9, 2)

M' = (2(-2) - (-2), 1) = ( -4 + 2, 1) = (-2, 1)

O' = (2(-2) - (-3), 3) = (-4 + 3, 3) = (-1, 3)

Therefore, the image vertices of N'M'O' after reflecting the preimage over x = -2 are N'(9, 2), M'(-2, 1), O'(-1, 3). So the answer is option (c): N′(1, 2), M′(−2, 1), O′(−1, 3).