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)

the answer is (8,14)

can you guys give me some answers

c'mon I don't see any answers y'all?

To find the coordinates of point B, we need to know that the diameter of a circle passes through the center of the circle. So, the midpoint of line segment AB will be the coordinates of the center of the circle.

1. Calculate the midpoint of line segment AB using the midpoint formula:
Midpoint = [(x1 + x2) / 2, (y1 + y2) / 2]

Given:
Point A coordinates: (4, 2)
Center coordinates: (6, 8)

Midpoint = [(4 + 6) / 2, (2 + 8) / 2]
= [10 / 2, 10 / 2]
= [5, 5]

The midpoint of line segment AB is (5, 5), which is the center of the circle.

2. Since the diameter of the circle passes through the center, we can use the midpoint to find the coordinates of point B.
Point A is (4, 2), and the center of the circle is (5, 5).
Point B will be on the same line as point A, but on the opposite side of the center.

To find the coordinates of point B, we can use the formula:
Point B = 2 * Center - Point A

Point B = 2 * (5, 5) - (4, 2)
= (10, 10) - (4, 2)
= (10 - 4, 10 - 2)
= (6, 8)

Therefore, the coordinates of point B are (6, 8).

If centre has (6,8) and one end of the diameter has (4,2), add Δx and Δy to the centre to get the other end of the diameter, namely,

(Δx,Δy) = (6-4, 8-2) = (2,6)
So the other end of the diameter would be (6+2,8+6)=(8,14).

Check: the mid-point of the diameter should be the centre:
((4+8)/2,(2+14)/2)=(6,8) = centre of circle.

Answer= (1,3)

(1,3)