## xRAWRRx3 3 years ago 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.

1. xRAWRRx3

|dw:1339302689432:dw|

2. Calcmathlete

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)

3. aceace

(x-3.5)^2 + (y-2)^2 = 6.5^2

4. xRAWRRx3

wait, I'm still confused about how to get it...

5. Calcmathlete

What are you confused on?

6. aceace

(x- the x co ordinate of c)^2 + (y- the y co ordinate of C) ^2 = the radius squared

7. Calcmathlete

Point C is the midpoint and therefore you can work backwards using the midpoint formula.

8. Calcmathlete

@aceace I think you misread the question...

9. xRAWRRx3

how do I work backwords though?

10. aceace

soory if i mis read the question

11. Calcmathlete

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)

12. Calcmathlete

Just focus on one of the values. FOr instance, what I did up there is start with x and then y.

13. Calcmathlete

Do you get it?\[M(x, y) = ((x_{1} + x_{2})/2, (y_{1} + y_{2})/2)\]

14. xRAWRRx3

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)

15. Calcmathlete

lol. Alright. You're welcome :)