anonymous
  • anonymous
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)
Geometry
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
@Owlcoffee
Owlcoffee
  • Owlcoffee
Are you fond to vectors?
anonymous
  • anonymous
Thanks

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anonymous
  • anonymous
No
anonymous
  • anonymous
Actually yes I am.
Owlcoffee
  • Owlcoffee
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: \[x_c-(-10)=12\] \[y_c - (-6)=6\]
anonymous
  • anonymous
Did it kick everyone offline?
Owlcoffee
  • Owlcoffee
No, just some changes in the website.
anonymous
  • anonymous
So it would be D?
Owlcoffee
  • Owlcoffee
no, solve the first equation for xc and the other for yc, that'll give you the coordinates of the point C
anonymous
  • anonymous
So B
Owlcoffee
  • Owlcoffee
correct.
anonymous
  • anonymous
When I said I was fond of vectors I ment in science...
anonymous
  • anonymous
Gave you a medal... Thanks so much.
Owlcoffee
  • Owlcoffee
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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