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Figure WXYZ is transformed using the rule . Point W of the pre-image is at (1, 6). What are the coordinates of point W" on the final image? (–5, 8) (–3, –8) (5, –8) (3, 8)

Respuesta :

danielmaduroh

Answer:

The final image is:

[tex]\boxed{W''(3,8)}[/tex]

Explanation:

Here we have two rules. The first one is a reflection across the y-axis and the second one is a translation. Let's apply these rules in two steps:

First rule:

Reflection across the y-axis:

[tex](x,y)\rightarrow (-x,y)[/tex]

By following this rule, you must multiply the x-coordinate of the point by -1. So here we reflect point W. Then:

[tex]W'(-1,6)[/tex]

Second rule:

[tex]T(x+4,y+2)[/tex]

This transformation shift each point 4 units to the right and 2 units up. Here we shift point W' that was previously transformed. Then:

[tex]W''(x,y)=W''(-1+4,6+2) \\ \\ \boxed{W''(x,y)=W''(3,8)}[/tex]

Applying the transformations, it is found that the coordinates of point W'' on the final image are (3, 8).

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  • The first transformation is a reflection across the y-axis, which has rule [tex](x,y) \rightarrow (-x,y)[/tex]
  • Applying for W(1,6), we get W'(-1,6).
  • The second transformation is a translation defined by [tex]T(x,y) \rightarrow T(x + 4, y + 2)[/tex].
  • Applying for W'(-1,6), we get W''(3,8), as [tex]-1 + 4 = 3[/tex] and [tex]6 + 2 = 8[/tex].

A similar problem is given at https://brainly.com/question/10547006

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