Question

M is the midpoint of AB. For each, given coordinates of point A and M. Find the coordinates of B.

A(4,6) and M(6,10)

Answer 1

To find point B given A(4,6) and midpoint M(6,10), we use the midpoint formula in reverse. The coordinates for B are calculated to be (8,14).

Step-by-step explanation:

To find the coordinates of point B given the midpoint M and point A, we use the midpoint formula in reverse. The midpoint M of AB is calculated by averaging the x and y coordinates of A and B. Since M is the midpoint, Mx = (Ax + Bx) / 2 and My = (Ay + By) / 2. Given that we have A(4,6) and M(6,10), we can set up equations for B's coordinates (Bx, By).

• For x: 6 = (4 + Bx) / 2, which gives Bx = 2(6) - 4 = 8.
• For y: 10 = (6 + By) / 2, which gives By = 2(10) - 6 = 14.

Therefore, the coordinates of point B are (8,14).