line segment ab is the diameter of circle O whose center has coordinates (6,8) . what are the coordinates of point b if the coordinates of point a are (4,2)
To determine the coordinates of point B, we need to consider that point A is the endpoint of the diameter of the circle while point B is the other endpoint. By using the midpoint formula for a line segment, we can find the midpoint of A and B, which will also be the center of the circle. Then, we can use this midpoint to find the coordinates of point B.
First, let's find the coordinates of the midpoint of line segment AB:
Midpoint formula: The midpoint of a line segment with endpoints (x1, y1) and (x2, y2) is given by the formula ((x1 + x2) / 2, (y1 + y2) / 2).
Given:
Point A = (4, 2)
Using the midpoint formula, we can find the midpoint of AB:
Midpoint = ((4 + x2) / 2, (2 + y2) / 2)
Since the center of the circle, O, is the midpoint of AB, we know that the center has coordinates (6, 8). Therefore, we can set up an equation using the coordinates of the midpoint and solve for x2 and y2:
((4 + x2) / 2, (2 + y2) / 2) = (6, 8)
Solving for x2:
(4 + x2) / 2 = 6
4 + x2 = 12
x2 = 12 - 4
x2 = 8
Solving for y2:
(2 + y2) / 2 = 8
2 + y2 = 16
y2 = 16 - 2
y2 = 14
Therefore, the coordinates of point B are (8, 14).