Question

Triangle NMO has vertices at N(−5, 2), M(−2, 1), O(−3 , 3). Determine the vertices of image N′M′O′ if the preimage is reflected over x = −4. N′(−3, 2), M′(−6, 1), O′(−5, 3) N′(−5, −6), M′(−2, −5), O′(−3, −7) N′(−5, −2), M′(−2, −3), O′(−3, −1) N′(−4, 2), M′(−1, 1), O′(−2, 3)

Answer 1

Notice that the reflection is over a line of the form x=constant; in this case, the y-coordinate of the reflected point stays the same while the x-coordinate changes as expressed by the transformation below

$\begin{gathered} y\rightarrow y \\ x\rightarrow2a+x \\ where \\ x=a\rightarrow\text{ vertical line} \end{gathered}$

Hence, in our case

$\Rightarrow(x,y)=(2*-4-x,y)=(-8-x,y)$

Transform points N, M, and O accordingly,

$\begin{gathered} \Rightarrow N^{\prime}=(-8-(-5),2)=(-8+5,2)=(-3,2) \\ \Rightarrow M^{\prime}=(-8-(-2),1)=(-6,1) \\ \Rightarrow O^{\prime}=(-8-(-3),3)=(-5,3) \end{gathered}$

Therefore, the answer is the first option (top to bottom)