Question

A circle on the coordinate plane has a diameter

with endpoints at (6, 8) and (15, 8).
a. What are the coordinates of the center of the
circle?
b. What is the diameter of the circle?
C. What is the radius of the circle?
d. Identify the coordinates of another point
on the circle. Explain how you found
your answer.

Answer 1

9514 1404 393

Answer:

a. (10.5, 8)

b. 9

c. 4.5

d. (10.5, 12.5)

Explanation:

a. The center of the circle is the midpoint of the diameter. Its coordinates are the average of the end point coordinates.

C = ((6,8) +(15, 8))/2 = (21, 16)/2 = (10.5, 8) . . . circle center

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b. The diameter lies on the horizontal line y=8, so its length is the difference of the x-coordinates of the end points: 15 -6 = 9 . . . circle diameter

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c. The radius is half the diameter: 9/2 = 4.5 . . . circle radius

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d. Another point on the circle will be 4.5 units from the center on the same vertical line: (10.5, 8) +(0, 4.5) = (10.5, 12.5) . . . another point on the circle