Question

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)

Answer 1

A (2 , 6)

B (4 , 2)

Reflection over x-axis general rule:

`P(x,y)\rightarrow P^(\prime)(x,-y)`

Dilation general rule:

`P(x,y)\rightarrow P^(\prime)(kx,ky)`

k is the scale factor

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If the line is reflected first:

`\begin{gathered} A(2,-6)\rightarrow A^(\prime)(2,6) \\ B(4,2)\rightarrow B^(\prime)(4,-2) \end{gathered}`

And then dilated by 1/2:

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

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If the line is dilated by 1/2:

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

And then reflected in the x-axis:

`\begin{gathered} A^(\prime)(1,-3)\rightarrow A^(\doubleprime)(1,3) \\ B^(\prime)(2,1)\rightarrow B^(\doubleprime)(2,-1) \end{gathered}`

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