Final answer:
To find the image of a point after a reflection over a line, we need to find the point that is the same distance from the line as the original point, but on the other side of the line. In this case, the line of reflection is y = -x, and the original point is (3, -2). The image of the point (3, -2) after a reflection over the line y = -x is (2, -3).
Step-by-step explanation:
To find the image of a point after a reflection over a line, we need to find the point that is the same distance from the line as the original point, but on the other side of the line. In this case, the line of reflection is y = -x, and the original point is (3, -2).
Now we need to find the point that is the same distance from the line y = -x as the original point (3, -2). We can do this by finding the equation of the line that is perpendicular to y = -x and passes through the original point (3, -2). The perpendicular line will have a slope of -1/(-1) = 1 and the equation of the line can be written as y - y1 = m(x - x1), where (x1, y1) is the original point. Substituting (3, -2) and m = 1, we get the equation y + 2 = (x - 3).
Now we find the intersection point of the two lines y = -x and y + 2 = (x - 3). Solving these equations simultaneously, we get x = 2 and y = -3. Therefore, the image of the point (3, -2) after a reflection over the line y = -x is (2, -3).