Question

What is the image of the point P (-3, 2) under a translation by the vector (-5, 7)?

a) The image of the point P is (-8, 9).
b) The image of the point P is (-10, 5).
c) The image of the point P is (2, -5).
d) The image of the point P is (-7, 9).

Answer 1

The image of the point P (-3, 2) after translation by the vector (-5, 7) is (-8, 9).

Step-by-step explanation:

The student is asking about the image of a point after a translation by a given vector. Specifically, the question is what the image of the point P (-3, 2) would be after a translation by the vector (-5, 7). To find the image of a point after a translation, we simply add the corresponding components of the point and the vector. Therefore, the x-coordinate of the image is -3 + (-5) = -8, and the y-coordinate is 2 + 7 = 9. Consequently, the image of the point P after the translation is the point (-8, 9).