Final answer:
To find the coordinates of point B when (4,2) is the midpoint and point A is (0,0), we use the midpoint formula. By solving the equations, we find that the coordinates of point B are (8,4).
Step-by-step explanation:
To determine the coordinates of point B given that (4,2) is the midpoint of segment AB and one endpoint (point A) is at (0,0), we need to use the midpoint formula which is (x1 + x2)/2, (y1 + y2)/2 for calculating the midpoint of a segment given the endpoints A(x1, y1) and B(x2, y2). Since we have the midpoint's coordinates and one endpoint, we can solve for the other endpoint.
Let's denote point B's coordinates as (xB, yB). According to the midpoint formula, we have:
(0 + xB)/2 = 4 and (0 + yB)/2 = 2. Solving these equations gives us xB = 8 and yB = 4.
Therefore, the coordinates of point B are (8,4).