Question

Line segment AB has endpoint A(-2, 3) and midpoint M(4, 6). Find the coordinates (x, y) of point B (the other endpoint).

Answer 1

Using the midpoint formula, the coordinates of endpoint B are found to be (10, 9).

Step-by-step explanation:

To find the coordinates of point B, we can use the concept that the midpoint formula gives us the average of the x-coordinates and y-coordinates of the endpoints of a line segment. Since we have one endpoint A(-2, 3) and the midpoint M(4, 6), we can set up equations to solve for the coordinates of B.

The midpoint M's x-coordinate is the average of A's and B's x-coordinates:
(-2 + xB) / 2 = 4. Solving for xB, we get xB = 4 * 2 + 2 = 10.

Similarly, the midpoint M's y-coordinate is the average of A's and B's y-coordinates:
(3 + yB) / 2 = 6. Solving for yB, we get yB = 6 * 2 - 3 = 9.

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