Question

geometry b
9.1 translations (worksheet)
graph the image of the figure using the transformation given.

1. translation: 4 units right and 1 unit down
2. translation: 5 units left
3. translation: 2 units right
4. translation: 5 units left
5. translation: (x, y)→(x + 1, y + 2)
6. translation: (x, y)→(x - 2, y - 2)

Explanation:

Step1: Recall translation rules

For a translation of $a$ units right and $b$ units down, the rule for a point $(x,y)$ is $(x + a,y - b)$. For $a$ units left and $b$ units up, the rule is $(x - a,y + b)$. For a general rule $(x,y)\to(x + m,y + n)$, we add $m$ to the $x$-coordinate and $n$ to the $y$-coordinate of each vertex of the figure.

Step2: Apply rules to vertices

1. For "4 units right and 1 unit down": If a vertex has coordinates $(x,y)$, its new coordinates are $(x + 4,y - 1)$. Plot the new - positioned vertices and connect them to get the translated figure.
2. For "5 units left": If a vertex has coordinates $(x,y)$, its new coordinates are $(x-5,y)$. Plot the new - positioned vertices and connect them.
3. For "2 units right": If a vertex has coordinates $(x,y)$, its new coordinates are $(x + 2,y)$. Plot the new - positioned vertices and connect them.
4. For "5 units left": If a vertex has coordinates $(x,y)$, its new coordinates are $(x-5,y)$. Plot the new - positioned vertices and connect them.
5. For $(x,y)\to(x + 1,y + 2)$: For each vertex $(x,y)$ of the original figure, find the new vertex $(x + 1,y + 2)$. Plot these new vertices and connect them.
6. For $(x,y)\to(x - 2,y - 2)$: For each vertex $(x,y)$ of the original figure, find the new vertex $(x - 2,y - 2)$. Plot these new vertices and connect them.

Since this is a graph - based problem, the actual answer would be the correctly - plotted translated figures on the given coordinate grids. But the general steps to achieve the answer are as above. In a practical sense, you would take each vertex of the original figure, apply the appropriate translation rule, and then redraw the figure using the new vertices.

Answer:

Step1: Recall translation rules

For a translation of $a$ units right and $b$ units down, the rule for a point $(x,y)$ is $(x + a,y - b)$. For $a$ units left and $b$ units up, the rule is $(x - a,y + b)$. For a general rule $(x,y)\to(x + m,y + n)$, we add $m$ to the $x$-coordinate and $n$ to the $y$-coordinate of each vertex of the figure.

Step2: Apply rules to vertices

1. For "4 units right and 1 unit down": If a vertex has coordinates $(x,y)$, its new coordinates are $(x + 4,y - 1)$. Plot the new - positioned vertices and connect them to get the translated figure.
2. For "5 units left": If a vertex has coordinates $(x,y)$, its new coordinates are $(x-5,y)$. Plot the new - positioned vertices and connect them.
3. For "2 units right": If a vertex has coordinates $(x,y)$, its new coordinates are $(x + 2,y)$. Plot the new - positioned vertices and connect them.
4. For "5 units left": If a vertex has coordinates $(x,y)$, its new coordinates are $(x-5,y)$. Plot the new - positioned vertices and connect them.
5. For $(x,y)\to(x + 1,y + 2)$: For each vertex $(x,y)$ of the original figure, find the new vertex $(x + 1,y + 2)$. Plot these new vertices and connect them.
6. For $(x,y)\to(x - 2,y - 2)$: For each vertex $(x,y)$ of the original figure, find the new vertex $(x - 2,y - 2)$. Plot these new vertices and connect them.

Since this is a graph - based problem, the actual answer would be the correctly - plotted translated figures on the given coordinate grids. But the general steps to achieve the answer are as above. In a practical sense, you would take each vertex of the original figure, apply the appropriate translation rule, and then redraw the figure using the new vertices.