To solve this problem, we first need to understand what it means to map one point to another through translation. In this case, the point (3, 2) is transformed to (4, 5). We can determine the translation vector by subtracting the coordinates of the original point from the coordinates of the image point.
The translation vector v can be calculated as follows:
- Translation vector v = (4 – 3, 5 – 2) = (1, 3)
This tells us that every point in this translation shifts 1 unit to the right and 3 units up.
To find the image of the point (2, 4) under the same translation, we apply the translation vector to this point:
- New point = (2 + 1, 4 + 3) = (3, 7)
Thus, the image of the point (2, 4) after applying the translation is (3, 7).