Question

write a geometric function that describes each translation.

1. function: \\((x, y) \

ightarrow (x+7, y+5)\\)

1. function: \\((x, y) \

ightarrow (x-5, y-5)\\)

1. function: \\((x, y) \

ightarrow (x-7, y+2)\\)

1. function: \\((x, y) \

ightarrow (x, y)\\)

1. function:
2. function:

Explanation:

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<reasoning>

Identify translation vector for Question 7

Using the Geometric Translations and Coordinate Rules for Transformations knowledge points

• Pre-image vertex \(A\) is at \((-3, 5)\).
• Image vertex \(A'\) is at \((4, 0)\).
• The translation rule is \((x, y)

ightarrow (x + a, y + b)\).

• Calculate \(a = 4 - (-3) = 7\) and \(b = 0 - 5 = -5\).
• The function is \((x, y)

ightarrow (x + 7, y - 5)\).

Identify translation vector for Question 8

Using the Geometric Translations and Coordinate Rules for Transformations knowledge points

• Pre-image vertex \(B\) is at \((4, -2)\).
• Image vertex \(B'\) is at \((-1, 3)\).
• Calculate \(a = -1 - 4 = -5\) and \(b = 3 - (-2) = 5\).
• The function is \((x, y)

ightarrow (x - 5, y + 5)\).

Identify translation vector for Question 9

Using the Geometric Translations and Coordinate Rules for Transformations knowledge points

• Pre-image vertex \(Y\) is at \((1, 5)\).
• Image vertex \(Y'\) is at \((-1, -1)\).
• Calculate \(a = -1 - 1 = -2\) and \(b = -1 - 5 = -6\).
• The function is \((x, y)

ightarrow (x - 2, y - 6)\).

Identify translation vector for Question 10

Using the Geometric Translations and Coordinate Rules for Transformations knowledge points

• Pre-image vertex \(D\) is at \((-4, 2)\).
• Image vertex \(D'\) is at \((-1, 5)\).
• Calculate \(a = -1 - (-4) = 3\) and \(b = 5 - 2 = 3\).
• The function is \((x, y)

ightarrow (x + 3, y + 3)\).

Identify translation vector for Question 11 and 12

Using the Geometric Translations and Coordinate Rules for Transformations knowledge points

• For Question 11: Pre-image vertex \(I\) is at \((-5, 4)\). Image vertex \(I'\) is at \((1, 5)\).
• Calculate \(a = 1 - (-5) = 6\) and \(b = 5 - 4 = 1\).
• The function is \((x, y)

ightarrow (x + 6, y + 1)\).

• For Question 12: Pre-image vertex \(X\) is at \((5, 5)\). Image vertex \(X'\) is at \((1, 2)\).
• Calculate \(a = 1 - 5 = -4\) and \(b = 2 - 5 = -3\).
• The function is \((x, y)

ightarrow (x - 4, y - 3)\).
</reasoning>

<answer>

No.	Answer

| 7 | \((x, y)
ightarrow (x + 7, y - 5)\) |
| 8 | \((x, y)
ightarrow (x - 5, y + 5)\) |
| 9 | \((x, y)
ightarrow (x - 2, y - 6)\) |
| 10 | \((x, y)
ightarrow (x + 3, y + 3)\) |
| 11 | \((x, y)
ightarrow (x + 6, y + 1)\) |
| 12 | \((x, y)
ightarrow (x - 4, y - 3)\) |
</answer>

<post_analysis>
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"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Geometry",
"Geometric Translations"
]
}
</post_analysis>

Answer:

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"needs_drawing": false,
"concepts_used": [
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"new_concepts": [],
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</pre_analysis>

<reasoning>

Identify translation vector for Question 7

Using the Geometric Translations and Coordinate Rules for Transformations knowledge points

• Pre-image vertex \(A\) is at \((-3, 5)\).
• Image vertex \(A'\) is at \((4, 0)\).
• The translation rule is \((x, y)

ightarrow (x + a, y + b)\).

• Calculate \(a = 4 - (-3) = 7\) and \(b = 0 - 5 = -5\).
• The function is \((x, y)

ightarrow (x + 7, y - 5)\).

Identify translation vector for Question 8

Using the Geometric Translations and Coordinate Rules for Transformations knowledge points

• Pre-image vertex \(B\) is at \((4, -2)\).
• Image vertex \(B'\) is at \((-1, 3)\).
• Calculate \(a = -1 - 4 = -5\) and \(b = 3 - (-2) = 5\).
• The function is \((x, y)

ightarrow (x - 5, y + 5)\).

Identify translation vector for Question 9

Using the Geometric Translations and Coordinate Rules for Transformations knowledge points

• Pre-image vertex \(Y\) is at \((1, 5)\).
• Image vertex \(Y'\) is at \((-1, -1)\).
• Calculate \(a = -1 - 1 = -2\) and \(b = -1 - 5 = -6\).
• The function is \((x, y)

ightarrow (x - 2, y - 6)\).

Identify translation vector for Question 10

Using the Geometric Translations and Coordinate Rules for Transformations knowledge points

• Pre-image vertex \(D\) is at \((-4, 2)\).
• Image vertex \(D'\) is at \((-1, 5)\).
• Calculate \(a = -1 - (-4) = 3\) and \(b = 5 - 2 = 3\).
• The function is \((x, y)

ightarrow (x + 3, y + 3)\).

Identify translation vector for Question 11 and 12

Using the Geometric Translations and Coordinate Rules for Transformations knowledge points

• For Question 11: Pre-image vertex \(I\) is at \((-5, 4)\). Image vertex \(I'\) is at \((1, 5)\).
• Calculate \(a = 1 - (-5) = 6\) and \(b = 5 - 4 = 1\).
• The function is \((x, y)

ightarrow (x + 6, y + 1)\).

• For Question 12: Pre-image vertex \(X\) is at \((5, 5)\). Image vertex \(X'\) is at \((1, 2)\).
• Calculate \(a = 1 - 5 = -4\) and \(b = 2 - 5 = -3\).
• The function is \((x, y)

ightarrow (x - 4, y - 3)\).
</reasoning>

<answer>

No.	Answer

| 7 | \((x, y)
ightarrow (x + 7, y - 5)\) |
| 8 | \((x, y)
ightarrow (x - 5, y + 5)\) |
| 9 | \((x, y)
ightarrow (x - 2, y - 6)\) |
| 10 | \((x, y)
ightarrow (x + 3, y + 3)\) |
| 11 | \((x, y)
ightarrow (x + 6, y + 1)\) |
| 12 | \((x, y)
ightarrow (x - 4, y - 3)\) |
</answer>

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"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Geometry",
"Geometric Translations"
]
}
</post_analysis>