Question

name:
major grade: transformations (reflection)
graph the image of the figure using the transformation given.

1. reflection across the x - axis (color red) then y - axis (color green)
2. reflection across the y - axis (green) then x - axis (red)
3. reflection across y = x
4. reflection across y = x

Explanation:

Step1: Recall reflection rules

• Reflection across x - axis: $(x,y)\to(x, - y)$. Reflection across y - axis: $(x,y)\to(-x,y)$. Reflection across $y = x$: $(x,y)\to(y,x)$.

Step2: For the first figure (left - top)

1. First, reflect across the x - axis. For each vertex $(x,y)$ of the original triangle, change it to $(x, - y)$. Then color it red.
2. Then, take the red - colored reflected figure and reflect it across the y - axis. For each vertex $(x,y)$ of the red - colored figure, change it to $(-x,y)$ and color it green.

Step3: For the second figure (right - top)

1. First, reflect across the y - axis. For each vertex $(x,y)$ of the original triangle, change it to $(-x,y)$. Color it green.
2. Then, take the green - colored reflected figure and reflect it across the x - axis. For each vertex $(x,y)$ of the green - colored figure, change it to $(x, - y)$ and color it red.

Step4: For the third and fourth figures

For each vertex $(x,y)$ of the original polygons, change it to $(y,x)$ to reflect across the line $y = x$.

Since this is a graph - based problem and we are not providing the actual graph here (as it requires drawing), the steps above describe the process of performing the reflections. To actually solve it, one would need to identify the coordinates of the vertices of the original figures on the grid and then apply the above - mentioned transformation rules to find the coordinates of the reflected vertices and draw the new figures accordingly.

Answer:

Follow the step - by - step reflection rules as described above to graph the images of the given figures for each transformation.