a diameter of a circle has endpoints at (1,2) and (-4,-6). what are the cordinates of the center of the circle?
To find the coordinates of the center of the circle, we can use the midpoint formula. The midpoint of a line segment with endpoints (x1, y1) and (x2, y2) is calculated using the following formula:
Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)
In this case, the endpoints of the diameter are (1, 2) and (-4, -6).
Let's calculate the midpoint:
x-coordinate of the midpoint = (1 + -4) / 2 = -3 / 2 = -1.5
y-coordinate of the midpoint = (2 + -6) / 2 = -4 / 2 = -2
Therefore, the coordinates of the center of the circle are (-1.5, -2).
To find the coordinates of the center of a circle, you need to find the midpoint of its diameter.
The midpoint formula states that the coordinates of the midpoint of a line segment with endpoints (x₁, y₁) and (x₂, y₂) are given by:
Midpoint = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)
In this case, the endpoints of the diameter are (1,2) and (-4,-6). Apply the midpoint formula:
Midpoint = ((1 + -4) / 2, (2 + -6) / 2)
= (-3/2, -4/2)
= (-3/2, -2)
Therefore, the coordinates of the center of the circle are (-3/2, -2).
the average of the endpoints:
x = (1-4)/2 = -3/2
y = (2-6)/2 = -2