Question

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.

Answer 1

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)

Answer 2

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

Answer 3

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

Answer 4

What are you confused on?

Answer 5

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

Answer 6

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

Answer 7

@aceace I think you misread the question...

Answer 8

how do I work backwords though?

Answer 9

soory if i mis read the question

Answer 10

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)

Answer 11

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

Answer 12

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

Answer 13

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)

Answer 14

lol. Alright. You're welcome :)