word problem involving points

[Obsession]

Consider the line segment whose endpoints are at (7,7) and (13,-2). There are two positions along this segment that cut it into two smaller segments whose respective lengths are in the ratio of 2 to 1. Through each of these two points lines are drawn through a third point (5,3).

Those two lines cross the line whose equation is x = 0 in two distinct points, respectively. What is the length of the segment formed by those two points?


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i would have tried to solve this, but i have no clue what its even asking me.


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also does anyone know where i can find this:
As we all know, the ratio of the cirumference of a circle to its diameter is represented by the greek letter pi. The ratio of the length of a rectangle to its width is represented by another greek letter. what is that letter?

 

[zerodegrees]

well......since they have given you coordinates, it would be an excellent idea to graph all the coordinates first.....before you do anything else. you know, one study tip is to draw a picture :idea:

 

[soroban]

Hello, Obsession!

Of course, you made sketch, didn't you?

Consider the line segment whose endpoints are at \(\displaystyle A(7,7)\) and \(\displaystyle B(13,-2).\)
There are two positions \(\displaystyle P\) and \(\displaystyle Q\) along this segment that cut it into two smaller segments
whose respective lengths are in the ratio of 2 to 1.
Through each of these two points lines are drawn through a third point \(\displaystyle R(5,3).\)

Those two lines cross the line whose equation is \(\displaystyle x\,=\,0\) in two distinct points, respectively.
What is the length of the segment formed by those two points?

        |                           * A(7,7)
        |
        |
        |                   R               * P(9,4)
        |                   *
        |                 (5,3)
        |                                           * Q(11,1)
    - - + - + - + - + - + - + - + - + - + - + - + - + - + - + - 
        |
        |                                                   * B(13,-2)
        |

Point \(\displaystyle P(9,4)\) divides \(\displaystyle AB\) so that \(\displaystyle \,APB\,=\,1:2\)
Point \(\displaystyle Q(11,1)\) divides \(\displaystyle AB\) so that \(\displaystyle \,AQ:QB\,=\,2:1\)

Find the equation of the line through \(\displaystyle P\) and \(\displaystyle R.\)
Find the equation of the line through \(\displaystyle Q\) and \(\displaystyle R.\)

These two lines have y-intercepts, \(\displaystyle M\) and \(\displaystyle N\), respectively.

Find the length of line segment \(\displaystyle MN.\)

As we all know, the ratio of the cirumference of a circle to its diameter
is represented by the Greek letter \(\displaystyle \pi\)
The ratio of the length of a rectangle to its width is represented by another Greek letter. ?
What is that letter?

Obviously, a rectangle does not have a constant length-width ratio.
Does the problem refer to a "Golden Rectangle"?

 

[Obsession]

Well good thing is that i had drawn a graph, i just didn't know what to do with it.
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Okay, I'm not sure if I did this right, so please don't hurt me if its wrong.

A(7,7)
B(13,-2)
P(9,4)
Q(11,1)
R(5,3)

Equation: y = mx + b or Ax+ By = C
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P and R

4-3 / 9 - 5 = 1 / 4
y= 1/4x + b
3 = 1/4(5) + b
3 = 1 1/4 + b
1 3/4 = b
y = 1/4x + 1 3/4
or
-x +4y = 5

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Q and R

1 - 3 / 11 - 5 = -2/6 = -1/3
y = -1/3x + b
3 = -1/3(5) + b
3 = -1 2/3 + b
4 2/3 = b
y = -1/3x + 4 2/3
x + 3y = 14
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Before you start yelling at me, I know its prob. wrong.

What do i do after that?


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Yeah, it does refer to the golden rectangle