Given
The coordinates of the triangle ABC are:
[tex]\begin{gathered} A\mleft(-2,-2\mright) \\ B(-6,\text{ -3)} \\ C(-1,\text{ -6)} \end{gathered}[/tex]
The coordinates of the triangle DEF are:
[tex]\begin{gathered} D(2,\text{ 2)} \\ E(6,\text{ 3)} \\ F(1,\text{ 6)} \end{gathered}[/tex]
The sequence of transformation that maps triangle ABC onto triangle DEF is
1. Reflection over the x-axis
The rule for the reflection over the x-axis:
[tex](x,\text{ y) }\rightarrow\text{ (x, -y)}[/tex]
Applying this rule to the triangle ABC gives:
[tex]\begin{gathered} A^{\prime}(-2,\text{ 2)} \\ B^{\prime}(-6,\text{ 3)} \\ C^{\prime}(-1,\text{ 6)} \end{gathered}[/tex]
2. Reflection over the y-axis:
The rule for the reflection over the y-axis:
[tex](x,\text{ y) }\rightarrow\text{ (-x, y)}[/tex]
Applying this gives :
[tex]\begin{gathered} A^{\prime}(-2,\text{ 2) }\rightarrow\text{ D(2, 2)} \\ B^{\prime}(-6,\text{ 3) }\rightarrow\text{ E(6, 3)} \\ C^{\prime}(-1,\text{ 6) }\rightarrow\text{ F(1, 6)} \end{gathered}[/tex]
Hence, the correct option is option A
