Question

#3 Choose the rule that represents a series of transformations

Answer 1

Step 1, write the coordinates of the vertices of the triangle GDI

$\begin{gathered} G\Rightarrow(2,-4) \\ D\Rightarrow(4,-1) \\ I\Rightarrow(5,-5) \end{gathered}$

Step 2: Write the coordinates of the vertices of the image G'D'I'

$\begin{gathered} G^{\prime}\Rightarrow(-5,6) \\ D^{\prime}\Rightarrow(-3,3) \\ I^{\prime}\Rightarrow(-2,7) \end{gathered}$

Step 3: Observe the difference in the x-coordinates to obtain the first rule of the transformation

$\begin{gathered} G^{\prime}-G\Rightarrow(-5-2)\Rightarrow-7 \\ D^{\prime}-D\Rightarrow(-3-4)\Rightarrow-7 \\ I^{\prime}-I\Rightarrow(-2-5)\Rightarrow-7 \\ \text{Thus,} \\ \text{The first order is } \\ (x-7,y) \end{gathered}$

Step 4: Reflect the resulting image over the x-axis

$\begin{gathered} (-5,-4)\Rightarrow(-5,4) \\ (-3,-1)\Rightarrow(-3,1) \\ (-2,-5)\Rightarrow(-2,5) \\ \text{The rule becomes } \\ (x-7,-y) \end{gathered}$

Step 5: Translate the resulting image vertically upward by 2 units

$\begin{gathered} (-5,4+2)\Rightarrow(-5,6) \\ (-3,1+2)\Rightarrow(-3,3) \\ (-2,5+2)\Rightarrow(-2,7) \\ \text{The rule after this sequence is} \\ (x-7,-y+2) \end{gathered}$

Hence, the rule that represents a series of transformations is given below

$(x,y)\Rightarrow(x-7,-y+2)$