We are asked to find the coordinates of point B given that point A has coordinates (2,4) and the midpoint M of the line AB has coordinates (3,0).
Given that the formula for calculating the midpoint of two points A and B in a Cartesian coordinate plane is M = [(x1 + x2) / 2, (y1 + y2) / 2] where:
- (x1, y1) are the coordinates of point A
- (x2, y2) are the coordinates of point B
Knowing point A and the midpoint M, we can rearrange the midpoint formula to find point B as follows:
- (x2, y2) = [2 * xM - x1, 2 * yM - y1] where M(xM, yM) is the midpoint.
Thus, substituting the given point A(2,4) and M(3,0) values into the rearranged midpoint formula we have:
- (x2, y2) = [2 * 3 - 2, 2 * 0 - 4]
Which simplifies to point B (4, -4). Therefore, the coordinates of point B are (4, -4).