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Asked Dec 15, 2019
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practice quuestion 23

23. Points (3, –3) and (7, 5) are endpoints of the diameter of a circle.
(a) What is the length of the diameter? Give the exact answer, simplified as much as possible.
Show work.
(b) What is the center point C of the circle?
(c) Given the point C you found in part (b), state the point symmetric to Cabout the y-axis.
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23. Points (3, –3) and (7, 5) are endpoints of the diameter of a circle. (a) What is the length of the diameter? Give the exact answer, simplified as much as possible. Show work. (b) What is the center point C of the circle? (c) Given the point C you found in part (b), state the point symmetric to Cabout the y-axis.

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Expert Answer

Step 1

The given endpoints are (3, –3) and (7,5).

Let (3, –3) be (x1, y1) and (7,5) be (x2, y2).

(a) The length of the diameter is,

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d = (x, - x, )' +(y; -,)* -/(7-3)° + (5-(-3)) = V4? + 8? = /16 + 64 /80 = 4/5 Thus, the length of the diameter is 4/5.

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Step 2

(b) The center point C of ...

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X + x, V, + y2 C = (h,k)=| (3+7 -3+5 10 2 = (5,1) Thus, center point C of the circle (h,k) is (5,1).

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