[tex]A^{\prime}^{\prime}(-6,-6)[/tex]
Explanation
Step 1
a) Plot the triangle
Step 2
now, do the transformations
Transformation 1
reflected across the y-axis:
The rule for a reflection over the y -axis is
[tex](x,y)\Rightarrow(-x,y)[/tex]
hence
[tex]\begin{gathered} A(2,-2)\Rightarrow reflected\text{ y-axis}\Rightarrow A^{\prime}(-2,-2) \\ B(-1,-1)\operatorname{\Rightarrow}reflected\text{y-ax}\imaginaryI\text{s}\operatorname{\Rightarrow}B^{\prime}(1,-1) \\ C(0,2)\operatorname{\Rightarrow}reflected\text{y-ax}\imaginaryI\text{s}\operatorname{\Rightarrow}C^{\prime}(0,2) \end{gathered}[/tex]
so
Step 3
transformation 2:
b)dilated by a factor of 3 with the origin as the center of dilation:
A dilation with scale factor k centered at the origin will take each point
and
[tex]P(x,y)\Rightarrow dilated\text{ \lparen}K\text{ is the factor\rparen}\Rightarrow P^{\prime}(kx,yx)[/tex]
so
in this case the factor is 3,hence
[tex]\begin{gathered} A^{\prime}(-2,-2)\Rightarrow dilated\text{ by a factor of 3}\Rightarrow A^{\prime}^{\prime}(-6,-6) \\ B^{\prime}(1,-1)\operatorname{\Rightarrow}dilated\text{ by a factor of 3}\Rightarrow B^{\prime}^{\prime}(3,-3) \\ C^{\prime}(0,2)\operatorname{\Rightarrow}dilated\text{ by a factor of 3}\Rightarrow C^{\prime^{\prime}}(0,6) \end{gathered}[/tex]
so,the coordinate of teh A'' is
[tex]A^{\prime}^{\prime}(-6,-6)[/tex]
I hope this helps you
