Final answer:
The friend's translation of point A is incorrect. The correct translation of moving point A 2 units down and 1 unit right should result in the point A'(4, -1), not A'(1, 2) as the friend has suggested.
Step-by-step explanation:
The student's friend states that they translate point A, which has coordinates (3,1), by moving it 2 units down and 1 unit to the right. The proper translation of point A under these transformations should yield a new point, A', with coordinates calculated as follows: we subtract 2 units from the y-coordinate and add 1 unit to the x-coordinate of point A.
Given the initial point A(3,1), the translation 2 units down means we should subtract 2 from the y-coordinate (1 - 2 = -1). The translation of 1 unit to the right means we should add 1 to the x-coordinate (3 + 1 = 4). Therefore, the correct translated point A' should be A'(4, -1).
However, the student's friend has erroneously calculated the new point as A'(1, 2). This suggests a translation of 2 units to the left (3 - 2) and 1 unit up (1 + 1), which is not what was purportedly intended. Therefore, the friend's translation is incorrect. To perform the correct translation, we should apply the changes to the coordinates as described: A'(3+1,1-2), which results in A'(4, -1).