https://file.aiquickdraw.com/mathbot/file/172668327073224hnugxa.jpg

The question asks to determine the coordinates of triangle \(ABC\) after a translation along the vector \(\langle 0, 2 \rangle\).

Given triangle \(ABC\) with the vertices:
- \(A(2, 0)\)
- \(B(-1, 5)\)
- \(C(4, 3)\)

The translation vector is \(\langle 0, 2 \rangle\), meaning that we add 0 to the x-coordinates and 2 to the y-coordinates of each vertex.

Let's compute the new coordinates after translation:

1. For point \(A(2, 0)\):
   - New coordinates: \(A'(2 + 0, 0 + 2) = A'(2, 2)\)

2. For point \(B(-1, 5)\):
   - New coordinates: \(B'(-1 + 0, 5 + 2) = B'(-1, 7)\)

3. For point \(C(4, 3)\):
   - New coordinates: \(C'(4 + 0, 3 + 2) = C'(4, 5)\)

Thus, the new coordinates of the vertices are:
- \(A'(2, 2)\)
- \(B'(-1, 7)\)
- \(C'(4, 5)\)

The correct answer is **C**.

Would you like more details on the translation process or any other questions? Here are some follow-up questions you might find useful:

1. What is the geometric meaning of a translation vector?
2. How would a different vector, such as \(\langle 3, -1 \rangle\), affect the coordinates of triangle \(ABC\)?
3. Can a translation change the shape or size of a figure?
4. What other transformations besides translation exist in coordinate geometry?
5. How do you find the result of multiple transformations applied sequentially?

**Tip:** Remember, a translation preserves the shape and size of the object—it only changes its position.

Triangle ABC has coordinates A(2, 0), B(-1, 5), and C(4, 3). Determine the coordinates of the vertices of the image after a translation along the vector ⟨0, 2⟩.

Learn how to calculate the coordinates of a triangle ABC after a translation by vector ⟨0, 2⟩. The problem focuses on coordinate geometry and vector translations. Suitable for students in Grades 6-8.

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