Final answer:
The new endpoints of a line segment that is shifted 2 units left and 5 units up are found by subtracting 2 from the x-coordinates and adding 5 to the y-coordinates of each original endpoint.
Step-by-step explanation:
To determine the new endpoints of a line segment after shifting it 2 units left and 5 units up, we need to apply this transformation to each endpoint of the original line segment. If the original endpoints are labeled (x1, y1) and (x2, y2), then after shifting, the new endpoints will be (x1 - 2, y1 + 5) and (x2 - 2, y2 + 5). The subtraction of 2 from the x-coordinates represents the leftward shift, while the addition of 5 to the y-coordinates accounts for the upward movement.