<u>Question</u>:
Parallelogram f"g"h"j" is the final image after the rule ry-axis • t1,2(x, y) was applied to parallelogram fghj. The coordinates are f''(3,4), g''(2,2), h''(4,2) and j''(5,4)
what are the coordinates of vertex f of parallelogram fghj?
(–2, 2)
(–2, 6)
(–3, 4)
(–4, 2)
<u>Given</u>:
Given that the the coordinates of the parallelogram f''g''h''j'' is the final image after the rule ry-axis • t1,2(x, y) was applied to parallelogram fghj.
The coordinates are f''(3,4), g''(2,2), h''(4,2) and j''(5,4)
We need to determine the coordinates of vertex f of parallelogram fghj.
<u>Reflection across y - axis:</u>
The general rule to reflect the coordinate across y - axis is given by
![(x,y) \rightarrow (-x,y)](https://tex.z-dn.net/?f=%28x%2Cy%29%20%5Crightarrow%20%28-x%2Cy%29)
Substituting the coordinate f''(3,4), we get;
![(3,4)\rightarrow (-3,4)](https://tex.z-dn.net/?f=%283%2C4%29%5Crightarrow%20%28-3%2C4%29)
Thus, the coordinates of f'' of reflection across the y - axis is (-3,4)
<u>Translation T1,2(x, y):</u>
The translation can be performed using the rule,
![T_{1,2}(x,y)=(x+1,y+2)](https://tex.z-dn.net/?f=T_%7B1%2C2%7D%28x%2Cy%29%3D%28x%2B1%2Cy%2B2%29)
Now, substituting the coordinate (-3,4), we get;
![T_{1,2}(-3,4)=(-3+1,4+2)](https://tex.z-dn.net/?f=T_%7B1%2C2%7D%28-3%2C4%29%3D%28-3%2B1%2C4%2B2%29)
![T_{1,2}(-3,4)=(-2,6)](https://tex.z-dn.net/?f=T_%7B1%2C2%7D%28-3%2C4%29%3D%28-2%2C6%29)
Thus, the coordinates of vertex F is (-2,6)
Hence, Option b is the correct answer.