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The midpoint of (segment)AB is M(7,5). The coordinates of point A are (4,1). Find the coordinates of point B.

Sure! To find the coordinates of point B, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint (M) can be found by taking the average of the coordinates of the two endpoints.

In this case, the coordinates of point M are given as (7,5). The coordinates of point A are given as (4,1).

Let's label the coordinates of point B as (x, y). Since the midpoint is the average of the endpoints, we can set up the following equations:

(x-coordinate of A + x-coordinate of B) / 2 = x-coordinate of M
(4 + x) / 2 = 7

Simplifying the equation:
4 + x = 14
x = 10

Similarly, we can set up the equation for the y-coordinate:

(y-coordinate of A + y-coordinate of B) / 2 = y-coordinate of M
(1 + y) / 2 = 5

Simplifying the equation:
1 + y = 10
y = 9

Therefore, the coordinates of point B are (10, 9).