Question:
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)
Given:
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.
Reflection across y - axis:
The general rule to reflect the coordinate across y - axis is given by
[tex](x,y) \rightarrow (-x,y)[/tex]
Substituting the coordinate f''(3,4), we get;
[tex](3,4)\rightarrow (-3,4)[/tex]
Thus, the coordinates of f'' of reflection across the y - axis is (-3,4)
Translation T1,2(x, y):
The translation can be performed using the rule,
[tex]T_{1,2}(x,y)=(x+1,y+2)[/tex]
Now, substituting the coordinate (-3,4), we get;
[tex]T_{1,2}(-3,4)=(-3+1,4+2)[/tex]
[tex]T_{1,2}(-3,4)=(-2,6)[/tex]
Thus, the coordinates of vertex F is (-2,6)
Hence, Option b is the correct answer.
