A diameter of a circle has endpoints at (4, 6) and the origin. Which point is also on the circle?
A. (–1, 2) B. (6, 3) C. (5, 0) D. (–1, 1) E. NOTA
Please explain.

- anonymous

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- campbell_st

find the midpoint x = (4 + 0)/2 y = (6 + 0)/2 that will give the centre

- campbell_st

then the equation is (x - h)^2 + (y-k)^2 = r^2 in this case r^2 = 52
(h, k) is the centre...
sub in each point... to test

- anonymous

answer is D (-1,1) please can you show more steps

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## More answers

- anonymous

I didn't get it

- Directrix

|dw:1328772724764:dw|

- anonymous

Please explain and show me the steps

- anonymous

lol beauty picture

- Directrix

@Sammy - I lost power but have returned to explain the problem.

- anonymous

after getting midpoint what to do

- anonymous

Thank you so much Directrix.

- Directrix

The midpoint of the diameter is the center of the circle.
One-half the length of the diameter is the radius of the circle..
We need that for the general equation of the circle:
(x - h)^2 + (y-k)^2 = r^2 and then ...

- Directrix

From (0,0) to (2,3) is the length we need.
The distance formula gives r = Square root[ ( 2 - 0)^2 + 3 - 0)^2]
r = Square Root [ 4 + 9] = Square root of 13.
And, then ...

- Directrix

r = √ 13 and (h,k) = (2,3)

- Directrix

(x - h)^2 + (y-k)^2 = r^2
(x - 2) ^2 + (y - 3) ^ 2 = (√ 13) ^2
(x - 2) ^2 + (y - 3) ^ 2
Option checking time now ...

- Directrix

(x - 2) ^2 + (y - 3) ^ 2
I am testing the D option
D. (–1, 1)
In the circle equation, substitute -1 for x and 1 for y and see if the left side = the right side of 13.

- Directrix

(x - 2) ^2 + (y - 3) ^ 2
( (-1- 2)^2 + (1 - 3) ^2 = (-3) ^2 + (-2) ^2 = 9 + 4 = 13.
So, the point (-1,1) is on the circle.

- Directrix

Suppose we had tested option A. (–1, 2).
Then, ( (-1 -2) ^2 + ( 2 - 3) ^ 2 = (-3)^2 + (-1) ^2 = 9 + 1 = 10 which is not equal to 13. So, the point (-1,2) is NOT on the circle.

- Directrix

Questions?

- anonymous

yes.

- Directrix

OK

- anonymous

( (-1- 2)^2 + (1 - 3) ^2 = (-3) ^2 + (-2) ^2 = 9 + 4 = 13. but it's not sqrt13

- Directrix

Remember the formula
(x - 2) ^2 + (y - 3) ^ 2 = (√ 13) ^2
(x - 2) ^2 + (y - 3) ^ 2 = (√ 13) ^2)
The (√ 13) ^2 = 13.
We are testing against 13.

- anonymous

Thank you so much for explaining and your time

- Directrix

Any time. Glad to help.

- anonymous

Can I ask one more problem?

- Directrix

Okay

- Directrix

Is it already posted?

- anonymous

Twice an integer increased by fourteen is less than 5. What is the greatest solution? Please explain.
it's a multiple choice
A. -5
B.-4
c.-4.5
D.- 4.6
E.NOTA

- anonymous

I already posted.but I didn't get the correct answer

- anonymous

Answer is A

- Directrix

Let x = the integer
Then,
2x + 14 < 5

- Directrix

2x + 14 < 5
2x < 5 - 14
2x < -9

- Directrix

The answer is an integer. Remember that.
2x < -9
x < - 4.5
Option time.

- Directrix

What is the biggest integer LESS than - 4.5?

- Directrix

|dw:1328774992369:dw|

- anonymous

so it is -5

- Directrix

The biggest integer less than -4.5 is -5.

- anonymous

Thank you so much. I didn't think like that.

- Directrix

If the question had ended up as x >- 4.5, we would select the first integer to the right of -4.5 which would be -4. On a number line, always remember that the greater of two numbers lies to the right of the other.

- Directrix

"I didn't think like that."
The simplest things can be the most confusing.

- anonymous

That' right!

- anonymous

Thank you so much for your help!

- Directrix

You are welcome. Any time.

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