anonymous
  • anonymous
In the diagram below of circle C, QR is a diameter, and Q(1, 8) and C(3.5 , 2) are points on a coordinate plane. Find and state the coordinates of point R.
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
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anonymous
  • anonymous
Use the midpoint formula, but work back wards. (3.5, 2) = (x_1 + x_2/2, y_1 + y_2/2) (7, 4) = (1 + x_2, 8 + y_2) (6, -4) = (x_2, y_2) Therefore, (6, -4)
anonymous
  • anonymous
(x-3.5)^2 + (y-2)^2 = 6.5^2

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anonymous
  • anonymous
wait, I'm still confused about how to get it...
anonymous
  • anonymous
What are you confused on?
anonymous
  • anonymous
(x- the x co ordinate of c)^2 + (y- the y co ordinate of C) ^2 = the radius squared
anonymous
  • anonymous
Point C is the midpoint and therefore you can work backwards using the midpoint formula.
anonymous
  • anonymous
@aceace I think you misread the question...
anonymous
  • anonymous
how do I work backwords though?
anonymous
  • anonymous
soory if i mis read the question
anonymous
  • anonymous
3.5 = (1 + x)/2 7 = 1 + x x = 6 The x coordinate of R is 6. Then work with y. 2 = (8 + y)/2 4 = 8 + y y = -4 Therefore, the y-coordinate of R is -4. R(6, -4)
anonymous
  • anonymous
Just focus on one of the values. FOr instance, what I did up there is start with x and then y.
anonymous
  • anonymous
Do you get it?\[M(x, y) = ((x_{1} + x_{2})/2, (y_{1} + y_{2})/2)\]
anonymous
  • anonymous
OHHH. Oh I'm sorry, I was really confused from when you meant backwards but I get it now LOL thank you SO much x)
anonymous
  • anonymous
lol. Alright. You're welcome :)

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