Question

graph the image of the figure using the transformation given. 3) reflection across x = 2 4) reflection

Explanation:

Step1: Recall reflection formula

For a point $(x,y)$ reflected across the vertical line $x = a$, the new - point $(x',y')$ is given by the formula $x'=2a - x$ and $y'=y$. Here $a = 2$.

Step2: Take each vertex of the figure

Let's assume a vertex of the original figure has coordinates $(x,y)$. After reflection across $x = 2$, its new $x$ - coordinate $x'=2\times2 - x=4 - x$ and the $y$ - coordinate remains the same $y' = y$.

Step3: Plot the new vertices

Calculate the new coordinates for all vertices of the original figure using the above - mentioned formula and then connect the new vertices to get the reflected figure.

Since no specific figure is given with coordinates, the general steps for graphing the reflection of a figure across the line $x = 2$ are as above. To actually graph, one would need to identify the vertices of the original figure, apply the transformation formula $x'=4 - x,y' = y$ to each vertex, and then plot the new vertices and draw the figure.

Answer:

Step1: Recall reflection formula

For a point $(x,y)$ reflected across the vertical line $x = a$, the new - point $(x',y')$ is given by the formula $x'=2a - x$ and $y'=y$. Here $a = 2$.

Step2: Take each vertex of the figure

Let's assume a vertex of the original figure has coordinates $(x,y)$. After reflection across $x = 2$, its new $x$ - coordinate $x'=2\times2 - x=4 - x$ and the $y$ - coordinate remains the same $y' = y$.

Step3: Plot the new vertices

Calculate the new coordinates for all vertices of the original figure using the above - mentioned formula and then connect the new vertices to get the reflected figure.

Since no specific figure is given with coordinates, the general steps for graphing the reflection of a figure across the line $x = 2$ are as above. To actually graph, one would need to identify the vertices of the original figure, apply the transformation formula $x'=4 - x,y' = y$ to each vertex, and then plot the new vertices and draw the figure.