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The problem asks to find the image of point \( (1, 3) \) after a translation using the translation function \( T_{\langle -2, 1 \rangle} \).

In a translation, we move the point according to the translation vector \( \langle -2, 1 \rangle \). This vector means:

- Move the point 2 units to the left (since the x-component is -2).
- Move the point 1 unit up (since the y-component is 1).

Let's compute the new coordinates for the point \( (1, 3) \):

1. \( x \)-coordinate: \( 1 + (-2) = 1 - 2 = -1 \)
2. \( y \)-coordinate: \( 3 + 1 = 4 \)

Thus, the image of the point \( (1, 3) \) after the translation is \( (-1, 4) \).

Would you like further details or have any questions?

Here are 5 related questions:
1. What is a translation in geometry, and how is it applied?
2. How do you interpret translation vectors like \( \langle -2, 1 \rangle \)?
3. What happens if you apply multiple translations to a point?
4. How would the image change if the vector was \( \langle 2, -1 \rangle \)?
5. How do different transformations like reflection or rotation compare to translation?

**Tip:** When translating a point, always apply the vector components to the corresponding x and y coordinates of the point directly.

Use the function notation below to find the image after the translation. T_{<-2, 1>}(1, 3). The image is point (___, ___).

Learn how to find the translated image of point (1, 3) after applying the translation vector T_{<-2, 1>}. This step-by-step solution involves moving the point 2 units left and 1 unit up. Suitable for students in Grades 6-8.

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