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11)The Point (1, 8) was translated in the coordinate plane and then reflected across the x-axis. It's final image was had the coordinates (4, -3) Which of the following best describes the translation that occurred? A)a shift of 3 units to the right and 11 units down B)a shift of 8 units left and 2 units down C)a shift of three units to the right and 5 units down D) a shifted 2 units left and 4 units up

11The Point 1 8 was translated in the coordinate plane and then reflected across the xaxis Its final image was had the coordinates 4 3 Which of the following be class=

Respuesta :

To find out the original translation let's undo the transformations given.

First we need to undo the reflection across the x-axis. A reflection across the x-axis is:

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

Then, if we undo it we have:

[tex](4,-3)\rightarrow(4,3)[/tex]

Now, a translation is given by:

[tex](x,y)\rightarrow(x+a,y+b)[/tex]

Then, the original translation will be of the form:

[tex](1,8)\rightarrow(1+a,8+b)=(4,3)[/tex]

Then we have the equations:

[tex]\begin{gathered} 1+a=4 \\ 8+b=3 \end{gathered}[/tex]

Solving them we have that a=3 and b=-5.

This means that the translation is a shift of 3 units to the right and 5 units down. Therefore the answer is C.

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