Question

The center of a circle is (4, 6), and an endpoint of a diameter is (2, 5). What is the other endpoint of the diameter?
a. (0, 4)
b. (3, 5.5)
c. (6, 7)

Answer 1

the distance between the center and an endpoint of a diameter is the radius. So, just get the distance from center to the endpoint of a diameter then multiply it by 2

Answer 2

how?

Answer 3

let (4,6) be one endpoint and (2,5) another endpoint. use distance formula.
\[d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\]

Answer 4

by d i mean distance not diameter

Answer 5

to find the diameter just multiply it by 2
\[diameter = 2\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\]

Answer 6

i got \[\sqrt{5}\]

Answer 7

that's right. but that's just the distance from the center to one of the endpoint of the diameter. like i said, you have to multiply it by 2 to get the length of the diameter.

Answer 8

\[\sqrt{10} = \sqrt{5}\sqrt{2}?\]

Answer 9

multiply by 2. not square root 2.

Answer 10

yeah \[\sqrt{10}???? \sqrt{5}\sqrt{2}\] is just in simplified form? :S

Answer 11

you multiplied square root of 5 by square root of 2. you just multiply square root of 5 by 2 not square root of 2

Answer 12

so \[2 \sqrt{5}\]???

Answer 13

yes

Answer 14

but arent there 2 coordinates to find?

Answer 15

i forgot it was looking for a coordinate sorry.

Answer 16

so its not like this?

Answer 17

it's close....okay..it's not like that sorry...this uses midpoints instead

Answer 18

the center is the midpoint of the diameter. so let's say the other endpoint of the diameter is (x,y).

(4,6) is the midpoint of the segment from (x,y) to (2,5)
you know the formula for midpoint right?
\[m_x = \frac{x_1 + x_2}{2}\]
\[m_y = \frac{y_1 + y_2}{2}\]

Answer 19

so mx = 4
my = 6
x1 = x
y1 = y
x2 = 2
y2 = 5
now substitute

Answer 20

sorry for my earlier mistake

Answer 21

no worries :)