AB is a diameter of a circle with centre at origin.what are the coordinates of B if coordinate of A are (3,-4)?

To find the coordinates of point B, we need to understand that point B lies on the circle's circumference, and since AB is a diameter, it passes through the origin (0,0).

The radius of the circle is half the length of the diameter. In our case, the radius is half the distance between the origin and point A.

To calculate the distance between the origin and point A, we can use the distance formula:

Distance = √((x2 - x1)^2 + (y2 - y1)^2)

Using the coordinates of the origin (0,0) and point A (3,-4), we can substitute the values into the formula:

Distance = √((3 - 0)^2 + (-4 - 0)^2)
= √(3^2 + (-4)^2)
= √(9 + 16)
= √25
= 5

Therefore, the radius of the circle is 5 units.

Now, since AB is a diameter, the distance between A and B is twice the radius. So:

Distance(A to B) = 2 * Radius
= 2 * 5
= 10

To find the coordinates of point B, we need to move 10 units in the opposite direction from point A along the line segment AB.

Starting from the coordinates of point A (3,-4), we can move 10 units in the opposite direction:

x-coordinate of B = 3 - 10
= -7

y-coordinate of B = -4 - 10
= -14

Therefore, the coordinates of point B are (-7, -14).

Hmmm. If you mean the center is at 0,0 then the radius is 5, so I bet the other side is -3,4

Oops, my diagram didn't transmit as I had hoped...sorry. Joe

B is at (-3,4).

Let the "●" represent the origin on the diagrwm below.

B
|
|y=4
| x=3
|_ _ _●_ _ _
X = -3 |
|y = -4
|
|
A