SOLUTION: the equation of two adjacent sides of a parallelogram are x+2y = 0 and 3x + y +3 = 0. One vertex has coordinates (8,-7). Find an equation of each of the lines that contain the othe

Algebra ->  Parallelograms -> SOLUTION: the equation of two adjacent sides of a parallelogram are x+2y = 0 and 3x + y +3 = 0. One vertex has coordinates (8,-7). Find an equation of each of the lines that contain the othe      Log On


   

Question 174743: the equation of two adjacent sides of a parallelogram are x+2y = 0 and 3x + y +3 = 0. One vertex has coordinates (8,-7). Find an equation of each of the lines that contain the other two sides of the parallelogram.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
First I checked to make sure that the point (8,-7) is not
a solution to either equation. That means neither line
passes through that point. Now all I have to do is find
2 lines. Both have to pass through (8,-7), one line must
be parallel to x+%2B+2y+=+0 and the other must be
parallel to 3x+%2B+y+%2B+3+=+0
The general point-slope formula is
%28y+-+y%5B1%5D%29%2F%28x+-+x%5B1%5D%29+=+m where m is slope
-------------------
For line parallel to x+%2B+2y+=+0,
2y+=+-x
y+=+-%281%2F2%29%2Ax
%28y+-+%28-7%29%29%2F%28x+-+8%29+=+-%281%2F2%29
y+%2B+7+=+4+-+x%2F2
x%2F2+%2B+y+%2B+3+=+0
x+%2B+2y+%2B+6+=+0
--------------------
For line parallel to 3x+%2B+y+%2B+3+=+0,
y+=+-3x+-+3
%28y+-+%28-7%29%29%2F%28x+-+8%29+=+-3
y+%2B+7+=+24+-+3x
3x+%2B+y+-+17+=+0
--------------------
Now I'll plot all 4 lines to check solution:

It looks like a parallelogram, so OK