Question

translation
graph the image of the figure using the transformation given

1. translation: 4 units right and 1 unit up
2. translation: 1 unit left and 3 units up
3. translation: 3 units down
4. translation: 3 units right and 1 unit up
5. translation: 4 units right and 4 units down
6. translation: 2 units right and 3 units up

Explanation:

To solve these translation problems, we follow these steps for each figure:

1) Translation: 4 units right and 1 unit up

Step 1: Identify original vertices

Find the coordinates of each vertex of the original figure (e.g., triangle) from the grid.

Step 2: Apply translation rule

For a translation of \( (x + 4, y + 1) \), add 4 to the \( x \)-coordinate and 1 to the \( y \)-coordinate of each vertex.

Step 3: Plot new vertices

Mark the new coordinates on the grid and connect them to form the translated figure.

2) Translation: 1 unit left and 3 units up

Step 1: Identify original vertices

Determine the coordinates of each vertex of the original figure.

Step 2: Apply translation rule

For a translation of \( (x - 1, y + 3) \), subtract 1 from the \( x \)-coordinate and add 3 to the \( y \)-coordinate of each vertex.

Step 3: Plot new vertices

Mark the new coordinates and draw the translated figure.

3) Translation: 3 units down

Step 1: Identify original vertices

Find the coordinates of each vertex of the original figure.

Step 2: Apply translation rule

For a translation of \( (x, y - 3) \), subtract 3 from the \( y \)-coordinate of each vertex ( \( x \)-coordinate remains unchanged).

Step 3: Plot new vertices

Plot the new coordinates and form the translated figure.

4) Translation: 7 units right and 1 unit up

Step 1: Identify original vertices

Determine the coordinates of each vertex of the original figure.

Step 2: Apply translation rule

For a translation of \( (x + 7, y + 1) \), add 7 to the \( x \)-coordinate and 1 to the \( y \)-coordinate of each vertex.

Step 3: Plot new vertices

Mark the new coordinates and draw the translated figure.

5) Translation: 4 units right and 4 units down

Step 1: Identify original vertices

Find the coordinates of each vertex of the original figure.

Step 2: Apply translation rule

For a translation of \( (x + 4, y - 4) \), add 4 to the \( x \)-coordinate and subtract 4 from the \( y \)-coordinate of each vertex.

Step 3: Plot new vertices

Plot the new coordinates and connect them to form the translated figure.

6) Translation: 2 units right and 3 units up

Step 1: Identify original vertices

Determine the coordinates of each vertex of the original figure.

Step 2: Apply translation rule

For a translation of \( (x + 2, y + 3) \), add 2 to the \( x \)-coordinate and 3 to the \( y \)-coordinate of each vertex.

Step 3: Plot new vertices

Mark the new coordinates and draw the translated figure.

Final Answer (General Process)

For each translation, follow the steps: 1) Identify original vertices, 2) Apply the translation rule to each vertex, 3) Plot the new vertices and connect them. The translated figures will be the original figures shifted according to the given horizontal and vertical distances.

Answer:

To solve these translation problems, we follow these steps for each figure:

1) Translation: 4 units right and 1 unit up

Step 1: Identify original vertices

Find the coordinates of each vertex of the original figure (e.g., triangle) from the grid.

Step 2: Apply translation rule

For a translation of \( (x + 4, y + 1) \), add 4 to the \( x \)-coordinate and 1 to the \( y \)-coordinate of each vertex.

Step 3: Plot new vertices

Mark the new coordinates on the grid and connect them to form the translated figure.

2) Translation: 1 unit left and 3 units up

Step 1: Identify original vertices

Determine the coordinates of each vertex of the original figure.

Step 2: Apply translation rule

For a translation of \( (x - 1, y + 3) \), subtract 1 from the \( x \)-coordinate and add 3 to the \( y \)-coordinate of each vertex.

Step 3: Plot new vertices

Mark the new coordinates and draw the translated figure.

3) Translation: 3 units down

Step 1: Identify original vertices

Find the coordinates of each vertex of the original figure.

Step 2: Apply translation rule

For a translation of \( (x, y - 3) \), subtract 3 from the \( y \)-coordinate of each vertex ( \( x \)-coordinate remains unchanged).

Step 3: Plot new vertices

Plot the new coordinates and form the translated figure.

4) Translation: 7 units right and 1 unit up

Step 1: Identify original vertices

Determine the coordinates of each vertex of the original figure.

Step 2: Apply translation rule

For a translation of \( (x + 7, y + 1) \), add 7 to the \( x \)-coordinate and 1 to the \( y \)-coordinate of each vertex.

Step 3: Plot new vertices

Mark the new coordinates and draw the translated figure.

5) Translation: 4 units right and 4 units down

Step 1: Identify original vertices

Find the coordinates of each vertex of the original figure.

Step 2: Apply translation rule

For a translation of \( (x + 4, y - 4) \), add 4 to the \( x \)-coordinate and subtract 4 from the \( y \)-coordinate of each vertex.

Step 3: Plot new vertices

Plot the new coordinates and connect them to form the translated figure.

6) Translation: 2 units right and 3 units up

Step 1: Identify original vertices

Determine the coordinates of each vertex of the original figure.

Step 2: Apply translation rule

For a translation of \( (x + 2, y + 3) \), add 2 to the \( x \)-coordinate and 3 to the \( y \)-coordinate of each vertex.

Step 3: Plot new vertices

Mark the new coordinates and draw the translated figure.

Final Answer (General Process)

For each translation, follow the steps: 1) Identify original vertices, 2) Apply the translation rule to each vertex, 3) Plot the new vertices and connect them. The translated figures will be the original figures shifted according to the given horizontal and vertical distances.