Question

translations
graph the image of the figure using the transformation given.

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

Explanation:

Problem 1: Translation 5 units right and 1 unit up

Step 1: Identify coordinates of original points

Let's assume the coordinates of \( G \), \( T \), \( B \) (from the first graph):

• \( G \): Let's say \( G(-3, 0) \) (from the grid, left 3 on x, 0 on y)
• \( T(-1, 0) \) (left 1 on x, 0 on y)
• \( B(-3, -3) \) (left 3 on x, down 3 on y)

Step 2: Apply translation (right 5, up 1)

For a point \( (x, y) \), translation \( (x + 5, y + 1) \):

• \( G' \): \( (-3 + 5, 0 + 1) = (2, 1) \)
• \( T' \): \( (-1 + 5, 0 + 1) = (4, 1) \)
• \( B' \): \( (-3 + 5, -3 + 1) = (2, -2) \)

Step 3: Graph the new points

Plot \( G'(2,1) \), \( T'(4,1) \), \( B'(2,-2) \) and connect them to form the translated figure.

Problem 2: Translation 1 unit left and 2 units up (incomplete, but process similar)

Step 1: Identify coordinates of \( Y \), \( O \), \( M \) (second graph):

• \( Y(-4, 1) \), \( O(-1, -1) \), \( M(-4, -2) \) (example coordinates)

Step 2: Apply translation (left 1: \( x - 1 \), up 2: \( y + 2 \))

• \( Y' \): \( (-4 - 1, 1 + 2) = (-5, 3) \)
• \( O' \): \( (-1 - 1, -1 + 2) = (-2, 1) \)
• \( M' \): \( (-4 - 1, -2 + 2) = (-5, 0) \)

Step 3: Graph the new points

Problem 3: Translation 3 units down

Step 1: Identify coordinates of \( Q \), \( L \), \( U \) (third graph):

• \( Q(1, 3) \), \( L(4, 0) \), \( U(0, -1) \) (example coordinates)

Step 2: Apply translation (down 3: \( y - 3 \))

• \( Q' \): \( (1, 3 - 3) = (1, 0) \)
• \( L' \): \( (4, 0 - 3) = (4, -3) \)
• \( U' \): \( (0, -1 - 3) = (0, -4) \)

Step 3: Graph the new points

Problem 4: Translation 5 units right (incomplete, process similar)

Step 1: Identify coordinates of \( X \), \( I \), \( E \) (fourth graph):

• \( X(-3, -1) \), \( I(-3, -3) \), \( E(-2, -3) \) (example coordinates)

Step 2: Apply translation (right 5: \( x + 5 \))

• \( X' \): \( (-3 + 5, -1) = (2, -1) \)
• \( I' \): \( (-3 + 5, -3) = (2, -3) \)
• \( E' \): \( (-2 + 5, -3) = (3, -3) \)

Step 3: Graph the new points

Problem 5: Translation 4 units right and 4 units down

Step 1: Identify coordinates of \( J \), \( I \) (fifth graph, example):

• \( J(-5, 4) \), \( I(-1, 1) \) (and third vertex, say \( K(-5, 1) \))

Step 2: Apply translation (right 4: \( x + 4 \), down 4: \( y - 4 \))

• \( J' \): \( (-5 + 4, 4 - 4) = (-1, 0) \)
• \( I' \): \( (-1 + 4, 1 - 4) = (3, -3) \)
• \( K' \): \( (-5 + 4, 1 - 4) = (-1, -3) \)

Step 3: Graph the new points

Problem 6: Incomplete (translation: 2 units...), follow similar steps: identify coordinates, apply translation, graph.

(Note: For actual graphing, use the grid to find precise coordinates of each vertex, then apply the translation rule \( (x \pm a, y \pm b) \) where \( a, b \) are the translation units, then plot the new vertices and connect them.)

Final Answer (for Problem 1 as example translated coordinates):

Translated points for Problem 1: \( G'(2,1) \), \( T'(4,1) \), \( B'(2,-2) \) (graph these to see the image).

(For other problems, follow the same coordinate identification and translation process.)

Answer:

Problem 1: Translation 5 units right and 1 unit up

Step 1: Identify coordinates of original points

Let's assume the coordinates of \( G \), \( T \), \( B \) (from the first graph):

• \( G \): Let's say \( G(-3, 0) \) (from the grid, left 3 on x, 0 on y)
• \( T(-1, 0) \) (left 1 on x, 0 on y)
• \( B(-3, -3) \) (left 3 on x, down 3 on y)

Step 2: Apply translation (right 5, up 1)

For a point \( (x, y) \), translation \( (x + 5, y + 1) \):

• \( G' \): \( (-3 + 5, 0 + 1) = (2, 1) \)
• \( T' \): \( (-1 + 5, 0 + 1) = (4, 1) \)
• \( B' \): \( (-3 + 5, -3 + 1) = (2, -2) \)

Step 3: Graph the new points

Plot \( G'(2,1) \), \( T'(4,1) \), \( B'(2,-2) \) and connect them to form the translated figure.

Problem 2: Translation 1 unit left and 2 units up (incomplete, but process similar)

Step 1: Identify coordinates of \( Y \), \( O \), \( M \) (second graph):

• \( Y(-4, 1) \), \( O(-1, -1) \), \( M(-4, -2) \) (example coordinates)

Step 2: Apply translation (left 1: \( x - 1 \), up 2: \( y + 2 \))

• \( Y' \): \( (-4 - 1, 1 + 2) = (-5, 3) \)
• \( O' \): \( (-1 - 1, -1 + 2) = (-2, 1) \)
• \( M' \): \( (-4 - 1, -2 + 2) = (-5, 0) \)

Step 3: Graph the new points

Problem 3: Translation 3 units down

Step 1: Identify coordinates of \( Q \), \( L \), \( U \) (third graph):

• \( Q(1, 3) \), \( L(4, 0) \), \( U(0, -1) \) (example coordinates)

Step 2: Apply translation (down 3: \( y - 3 \))

• \( Q' \): \( (1, 3 - 3) = (1, 0) \)
• \( L' \): \( (4, 0 - 3) = (4, -3) \)
• \( U' \): \( (0, -1 - 3) = (0, -4) \)

Step 3: Graph the new points

Problem 4: Translation 5 units right (incomplete, process similar)

Step 1: Identify coordinates of \( X \), \( I \), \( E \) (fourth graph):

• \( X(-3, -1) \), \( I(-3, -3) \), \( E(-2, -3) \) (example coordinates)

Step 2: Apply translation (right 5: \( x + 5 \))

• \( X' \): \( (-3 + 5, -1) = (2, -1) \)
• \( I' \): \( (-3 + 5, -3) = (2, -3) \)
• \( E' \): \( (-2 + 5, -3) = (3, -3) \)

Step 3: Graph the new points

Problem 5: Translation 4 units right and 4 units down

Step 1: Identify coordinates of \( J \), \( I \) (fifth graph, example):

• \( J(-5, 4) \), \( I(-1, 1) \) (and third vertex, say \( K(-5, 1) \))

Step 2: Apply translation (right 4: \( x + 4 \), down 4: \( y - 4 \))

• \( J' \): \( (-5 + 4, 4 - 4) = (-1, 0) \)
• \( I' \): \( (-1 + 4, 1 - 4) = (3, -3) \)
• \( K' \): \( (-5 + 4, 1 - 4) = (-1, -3) \)

Step 3: Graph the new points

Problem 6: Incomplete (translation: 2 units...), follow similar steps: identify coordinates, apply translation, graph.

(Note: For actual graphing, use the grid to find precise coordinates of each vertex, then apply the translation rule \( (x \pm a, y \pm b) \) where \( a, b \) are the translation units, then plot the new vertices and connect them.)

Final Answer (for Problem 1 as example translated coordinates):

Translated points for Problem 1: \( G'(2,1) \), \( T'(4,1) \), \( B'(2,-2) \) (graph these to see the image).

(For other problems, follow the same coordinate identification and translation process.)