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anonymous

  • 4 years ago

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.

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  1. campbell_st
    • 4 years ago
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    find the midpoint x = (4 + 0)/2 y = (6 + 0)/2 that will give the centre

  2. campbell_st
    • 4 years ago
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    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

  3. anonymous
    • 4 years ago
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    answer is D (-1,1) please can you show more steps

  4. anonymous
    • 4 years ago
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    I didn't get it

  5. Directrix
    • 4 years ago
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    |dw:1328772724764:dw|

  6. anonymous
    • 4 years ago
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    Please explain and show me the steps

  7. anonymous
    • 4 years ago
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    lol beauty picture

  8. Directrix
    • 4 years ago
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    @Sammy - I lost power but have returned to explain the problem.

  9. anonymous
    • 4 years ago
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    after getting midpoint what to do

  10. anonymous
    • 4 years ago
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    Thank you so much Directrix.

  11. Directrix
    • 4 years ago
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    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 ...

  12. Directrix
    • 4 years ago
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    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 ...

  13. Directrix
    • 4 years ago
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    r = √ 13 and (h,k) = (2,3)

  14. Directrix
    • 4 years ago
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    (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 ...

  15. Directrix
    • 4 years ago
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    (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.

  16. Directrix
    • 4 years ago
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    (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.

  17. Directrix
    • 4 years ago
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    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.

  18. Directrix
    • 4 years ago
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    Questions?

  19. anonymous
    • 4 years ago
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    yes.

  20. Directrix
    • 4 years ago
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    OK

  21. anonymous
    • 4 years ago
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    ( (-1- 2)^2 + (1 - 3) ^2 = (-3) ^2 + (-2) ^2 = 9 + 4 = 13. but it's not sqrt13

  22. Directrix
    • 4 years ago
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    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.

  23. anonymous
    • 4 years ago
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    Thank you so much for explaining and your time

  24. Directrix
    • 4 years ago
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    Any time. Glad to help.

  25. anonymous
    • 4 years ago
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    Can I ask one more problem?

  26. Directrix
    • 4 years ago
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    Okay

  27. Directrix
    • 4 years ago
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    Is it already posted?

  28. anonymous
    • 4 years ago
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    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

  29. anonymous
    • 4 years ago
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    I already posted.but I didn't get the correct answer

  30. anonymous
    • 4 years ago
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    Answer is A

  31. Directrix
    • 4 years ago
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    Let x = the integer Then, 2x + 14 < 5

  32. Directrix
    • 4 years ago
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    2x + 14 < 5 2x < 5 - 14 2x < -9

  33. Directrix
    • 4 years ago
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    The answer is an integer. Remember that. 2x < -9 x < - 4.5 Option time.

  34. Directrix
    • 4 years ago
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    What is the biggest integer LESS than - 4.5?

  35. Directrix
    • 4 years ago
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    |dw:1328774992369:dw|

  36. anonymous
    • 4 years ago
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    so it is -5

  37. Directrix
    • 4 years ago
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    The biggest integer less than -4.5 is -5.

  38. anonymous
    • 4 years ago
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    Thank you so much. I didn't think like that.

  39. Directrix
    • 4 years ago
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    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.

  40. Directrix
    • 4 years ago
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    "I didn't think like that." The simplest things can be the most confusing.

  41. anonymous
    • 4 years ago
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    That' right!

  42. anonymous
    • 4 years ago
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    Thank you so much for your help!

  43. Directrix
    • 4 years ago
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    You are welcome. Any time.

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