On the xy-coordinate plane, point A and B both lie on the circumference of a circle whose center is o, and the length AB equals the circle's diameter. If the (x, y) coordinates of o are (2,1) and the (x, y) coordinates of B are (4,6). What are the (x, y) coordinates of A?

A(0, - 4)

Step-by-step explanation: line AB is the length of the diameter of the circle with center o.

Center o has the coordinate (2, 1)

Point B has the coordinate (4, 6)

Point A has the coordinate (x1, y1)

The coordinate of the midpoint ( center o) is defined by the formulae below.

x = (x2 + x1) /2 and y = (y2 + y1) /2

Where x and y are coordinates of the center point o with x = 2 and y = 1

For point B, we have that x2 = 4 and y2 = 6

By substituting the parameters, we have that

2 = (4 + x1) /2

By cross multiplying

2×2 = 4 + x1

4 = 4 + x1

x1 = 4 - 4

x1 = 0.

1 = (6 + y1) / 2

By cross multiplying, we have that

1 × 2 = 6 + y1

2 = 6 + y1

2 - 6 = y1

y1 = - 4.

Hence coordinates of point A is (0, - 4)