Final answer:
To find the image of (4,2) under the given translation that moved (-2, 3) to (3, -1), we apply the same horizontal and vertical shifts of +5 and -4, respectively, to get the new coordinates (9, -2).
Step-by-step explanation:
The student's question is about finding the image of a point under a given translation. The translation moves point (-2, 3) to (3, -1). To find the image of point (4, 2) under the same translation, we need to determine the horizontal and vertical shifts that occurred in the first translation.
First, to determine the horizontal shift:
Horizontal shift = New x-coordinate - Original x-coordinate
Horizontal shift = 3 - (-2)
Horizontal shift = 5 units to the right
Next, to determine the vertical shift:
Vertical shift = New y-coordinate - Original y-coordinate
Vertical shift = -1 - 3
Vertical shift = -4 units down.
Applying the same shifts to point (4,2) to determine its image:
New x-coordinate = Original x-coordinate + Horizontal shift
New x-coordinate = 4 + 5 = 9
New y-coordinate = Original y-coordinate + Vertical shift
New y-coordinate = 2 - 4 = -2
Therefore, the image of point (4,2) under the same translation is (9, -2), which corresponds to option A.