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anonymous

  • one year ago

Points A (-10,-6) and B (6,2) are the endpoints of AB. What are the coordinates of point C on AB such that AC is 3/4 the length of AB? a. (0,-1) b. (2,0) c. (-2,-2) d. (4,1)

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  1. anonymous
    • one year ago
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    @Owlcoffee

  2. Owlcoffee
    • one year ago
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    Are you fond to vectors?

  3. anonymous
    • one year ago
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    Thanks

  4. anonymous
    • one year ago
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    No

  5. anonymous
    • one year ago
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    Actually yes I am.

  6. Owlcoffee
    • one year ago
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    Okay, so I'll show you the vector way. We can express the vector whose tail is located on "A" and head on "B" like this: \[\vec a ((6-(-10)), (2-(-6))) \rightarrow \vec a (16,8)\] \(\vec a\) is a vector that goes from A to B, and we want to find a "C" on AB such that AC=3/4 the length of AB. This means a 3/4 part of the vector, this creates a new vector \(\vec w\) that is \(\frac{ 3 }{ 4 } \vec a\), but we can do it by expressing the vector on it's referential form: \[\vec a = 16 \vec i + 8 \vec j \rightarrow \frac{ 3 }{ 4 } \vec a = (\frac{ 3 }{ 4 } 16) \vec i + (\frac{ 3 }{ 4 }8) \vec j \] \[\frac{ 3 }{ 4 } \vec a = \vec w \] \[\vec w = (3.4) \vec i + (3.2)\vec j\] \[\vec w = 12 \vec i + 6 \vec j\] This implies that the new coordinates lie on \[\vec w (12,6)\] And this implies, regressing the operation of the vector, since the tail still lies on A, but the head is now on the point C: \[x_c-(-10)=12\] \[y_c - (-6)=6\]

  7. anonymous
    • one year ago
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    Did it kick everyone offline?

  8. Owlcoffee
    • one year ago
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    No, just some changes in the website.

  9. anonymous
    • one year ago
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    So it would be D?

  10. Owlcoffee
    • one year ago
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    no, solve the first equation for xc and the other for yc, that'll give you the coordinates of the point C

  11. anonymous
    • one year ago
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    So B

  12. Owlcoffee
    • one year ago
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    correct.

  13. anonymous
    • one year ago
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    When I said I was fond of vectors I ment in science...

  14. anonymous
    • one year ago
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    Gave you a medal... Thanks so much.

  15. Owlcoffee
    • one year ago
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    Oh.. Well, if I were to say the method wihout them, I would suggest you find the distance between those two points. Then multiply it by 3/4, and then the process is completely analogous.

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