# coordinate geometry help.

• Nov 19th 2008, 06:46 AM
milan
coordinate geometry help.
rtsu is a quadrilateral where r(-1, -5), s(13, 9), q(3, -1), u(-2k, 3k), t(x, y).
If k=2 and the slope of ts is -3/11 and sr is parallel to tu, find the coordinates of t.

In the book there is a drawing of the quadrilateral but i dont know how to put drawing so please draw it yourselves and try, i dont know what to use to find t? i tried using perp. distance but it doesnt work.
• Nov 19th 2008, 07:16 AM
earboth
Quote:

Originally Posted by milan
rtsu is a quadrilateral where r(-1, -5), s(13, 9), q(3, -1), u(-2k, 3k), t(x, y).
If k=2 and the slope of ts is -3/11 and sr is parallel to tu, find the coordinates of t.

...

r(-1, -5), u(-4, 6), s(13,9)

The slope of rs is:

$m_{r,s} = \dfrac{-5-9}{-1-13}=\dfrac{-14}{-14}=1$

Therefore the line through u parallel to rs has the equation:

$y-6=1\cdot (x-(-4))~\implies~\boxed{y=x+10}$

The line through s with the slope of $m=-\dfrac3{11}$ has the equation:

$y-9=-\dfrac3{11}(x-13)~\implies~\boxed{y=-\dfrac3{11}x+\dfrac{138}{11}}$

The intersection of these 2 lines is point t:

$-\dfrac3{11}x+\dfrac{138}{11}=x+10~\implies~x=2$

Therefore t(2, 12)