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Translate the point A(-3, 7) using the vector (-4, 6). What are the coordinates of the image?

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To solve the problem of translating point A with coordinates (-3, 7) by the vector (-4, 6), follow these steps:

1. Understand the concept of translation: Translation involves moving a point a certain distance in a given direction. This is done by adding the components of the vector to the coordinates of the point.

2. Identify the components:
- Initial coordinates of point A are [tex]\( A(-3, 7) \)[/tex].
- Translation vector is [tex]\( (-4, 6) \)[/tex].

3. Apply the translation to the x-coordinate:
- Initial x-coordinate of point A is [tex]\( -3 \)[/tex].
- The x-component of the vector is [tex]\( -4 \)[/tex].
- New x-coordinate is found by adding these: [tex]\( -3 + (-4) = -3 - 4 = -7 \)[/tex].

4. Apply the translation to the y-coordinate:
- Initial y-coordinate of point A is [tex]\( 7 \)[/tex].
- The y-component of the vector is [tex]\( 6 \)[/tex].
- New y-coordinate is found by adding these: [tex]\( 7 + 6 = 13 \)[/tex].

5. Combine the new coordinates:
The new coordinates of point A after translation are [tex]\( (-7, 13) \)[/tex].

Thus, the coordinates of the image after translating point A by the vector [tex]\( (-4, 6) \)[/tex] are [tex]\( (-7, 13) \)[/tex].
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