Final answer:
Given the midpoint M(3,7) and endpoint B(8,10), the coordinates for endpoint A are found using the midpoint formula and are A(-2,4).
Step-by-step explanation:
The student is asking for the coordinates of endpoint A given the midpoint M and endpoint B of a line segment. The midpoint of a line segment has a property that its coordinates are the averages of the corresponding coordinates of the endpoints. Given M(3,7) and B(8,10), we can use the formula for the midpoint M, which is M = ((Ax + Bx)/2, (Ay + By)/2) to find the coordinates of A.
Therefore, Ax = 2*Mx - Bx and Ay = 2*My - By, which results in Ax = 2*3 - 8 and Ay = 2*7 - 10. This simplifies to Ax = -2 and Ay = 4, so the coordinates of the endpoint A are A(-2,4).