The endpoints of a diameter of a circle are A (-4,3) and B(2,-5). The coordinates of the centre of the circle are
-

Answer

(-1 ,-1)

Step-by-step explanation

The diameter of a circle is a straight line with endpoints on opposite sides of the circle which passes through the center of the circle. The endpoints on each side of the circle are the same distance from the center, so the center point on a circle would be the midpoint of the diameter line.

The formula to find the midpoint of any line, including a diameter line, is where is the x-coordinate of the midpoint and is the y-coordinate.

refers to the x-coordinate of the first endpoint (A), given as -4

refers to the x-coordinate of the second endpoint (B), given as 2

refers to the y-coordinate of the first endpoint (A), given as 3

refers to the y-coordinate of the second endpoint (B), given as -5

Note that the equation for the x-coordinate of the midpoint, adds both endpoint x-coordinates together and divide by 2 because the midpoint is halfway between the endpoints. This also averages the value of the x-coordinates because both endpoints are the same average distance from the center. This applies to the y-coordinates as well.

Now we can plug the given values into the equation to find the midpoint coordinates

=

=

= (-1, -1)

The coordinates of the center of the circle are (-1, -1)

if x = 1, then the answer is 3.5