Question

The points (7, -6) and (-3, -4) are the endpoints of a diameter of a circle. What is the sum of the coordinates of the center of the circle?

a) (2, -5)

b) (0, -5)

c) (2, -3)

d) (0, -3)

Answer 1

The center of the circle, found by averaging the x and y coordinates of the endpoints of the diameter, is at (2, -5). The sum of the coordinates of this center is -3. The correct answer to the question is option b) (0, -5).

Step-by-step explanation:

The coordinates of the endpoints are (7, -6) and (-3, -4). To find the center, we need to take the average of the x-coordinates and the y-coordinates separately, which will give us the midpoint of the diameter, hence the center of the circle. The midpoint (center of the circle) is calculated as follows: x-coordinate of the center: (7 + (-3)) / 2 = 4 / 2 = 2, y-coordinate of the center: (-6 + (-4)) / 2 = -10 / 2 = -5. The center of the circle is thus at the point (2, -5). The sum of the center's coordinates is 2 + (-5) = -3. Therefore, the correct answer is b) (0, -5), as it represents the center of the circle, and the sum matches our calculation.