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The coordinates of the endpoints of AB are A(2,6) and B(4,2). Is the image A"B" the same if it is 1 reflected in the x-axis, then dilated by 5 as the 1 image is if it is dilated by then reflected in the 2 x-axis? Justify your answer. (The use of the accompanying grid is optional)

The coordinates of the endpoints of AB are A26 and B42 Is the image AB the same if it is 1 reflected in the xaxis then dilated by 5 as the 1 image is if it is d class=

Respuesta :

A (2 , 6)

B (4 , 2)

Reflection over x-axis general rule:

[tex]P(x,y)\rightarrow P^{\prime}(x,-y)[/tex]

Dilation general rule:

[tex]P(x,y)\rightarrow P^{\prime}(kx,ky)[/tex]

k is the scale factor

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If the line is reflected first:

[tex]\begin{gathered} A(2,-6)\rightarrow A^{\prime}(2,6) \\ B(4,2)\rightarrow B^{\prime}(4,-2) \end{gathered}[/tex]

And then dilated by 1/2:

[tex]\begin{gathered} \\ A^{\prime}(2,6)\rightarrow A^{\doubleprime}(1,3) \\ \\ \\ B^{\prime}(4,-2)\rightarrow B^{\doubleprime}(2,-1) \end{gathered}[/tex]

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If the line is dilated by 1/2:

[tex]\begin{gathered} A(2,-6)\rightarrow A^{\prime}(1,-3) \\ \\ B(4,2)\rightarrow B^{\prime}(2,1) \end{gathered}[/tex]

And then reflected in the x-axis:

[tex]\begin{gathered} A^{\prime}(1,-3)\rightarrow A^{\doubleprime}(1,3) \\ B^{\prime}(2,1)\rightarrow B^{\doubleprime}(2,-1) \end{gathered}[/tex]

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Then, the image A''B'' is the same in both cases

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