SOLUTION: Hi, I'm stuck on this equation. Parallelogram ABCD with vertices A=(1,2), B=(3,8), C= (9,0) and D= (x,y). Hint vector AB=vector DC. I'm really stuck and have no idea how to find x

Question 69345: Hi,
I'm stuck on this equation. Parallelogram ABCD with vertices A=(1,2), B=(3,8), C= (9,0) and D= (x,y). Hint vector AB=vector DC. I'm really stuck and have no idea how to find x and y. Please help. the answer's supposed to be (7,4)
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Parallelogram ABCD with vertices A=(1,2), B=(3,8), C= (9,0) and D= (x,y).
------------------------
Plot the points so you can visualize the position of D(x,y)
The first thing you should see is that (7,4) cannot be the right answer.
You need an equation for CD and an equation for BD
-------------------------
CD???
has the same slope as AB which is "3"
CD is the line with slope of 3 and passing through (9,0)
That equation is y=3x-27
----------------
BD????
has the same slope as AC which is -1/4
BD is the line with slope of 1/4 and passing through (3,8)
That equation is y=(-1/4)x+(35/4)
---------------
Setting 3x-27 = (-1/4)x+(35/4)
solve for x=11
Solve for y=6
----------------
Cheers,
Stan H.
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