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Select the sequence of transformations that will carry rectangle A onto rectangle A'. A) reflect over y-axis, rotate 90° clockwise, then reflect over x-axis B) rotate 180° clockwise, reflect over y-axis, then translate 3 units left C) rotate 180° clockwise, reflect over x-axis, then translate 2 units left D) rotate 90° clockwise, reflect over y axis, then translate 3 units left

Answer :

Let:

[tex]\begin{gathered} A=(3,4) \\ B=(4,2) \\ C=(1,-1) \end{gathered}[/tex]

and:

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

After a reflection over the y-axis:

[tex]\begin{gathered} A\to(-x,y)\to A_1=(-3,4) \\ B\to(-x,y)\to B_1=(-4,2) \\ C\to(-x,y)\to C_1=(-1,-1) \end{gathered}[/tex]

After a translation 3 units down:

[tex]\begin{gathered} A_1\to(x,y-3)\to A_2=(-3,1) \\ B_1\to(x,y-3)\to B_2=(-4,-1) \\ C_1\to(x,y-3)\to C_2=(-1,-4) \end{gathered}[/tex]

Since:

[tex]\begin{gathered} A_2=A^{\prime} \\ B_2=B^{\prime} \\ C_2=C^{\prime} \end{gathered}[/tex]

The answer is the option K.

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