SOLUTION: The coordinates of 3 of the vertices of a parallelogram are (–3, 4), (–2, 1), and (2, 6). What is the equation for the line containing the side opposite the side containing the fir

Algebra ->  Parallelograms -> SOLUTION: The coordinates of 3 of the vertices of a parallelogram are (–3, 4), (–2, 1), and (2, 6). What is the equation for the line containing the side opposite the side containing the fir      Log On


   

Question 742132: The coordinates of 3 of the vertices of a parallelogram are (–3, 4), (–2, 1), and (2, 6). What is the equation for the line containing the side opposite the side containing the first two vertices?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The slope of the line connecting (-3,4) and (-2,1) can be calculated as the difference of the y-coordinates divided by the difference of the x coordinates.
Subtracting the coordinates of (-3,4) minus the coordinates of (-2,1), we get
slope=m=%284-1%29%2F%28-3-%28-2%29%29=3%2F%28-3%2B2%29=3%2F%28-1%29=-3

The opposite side is parallel, and parallel lines have the same slope, so the line we want also has slope m=-3.

The equation of a line with slope -3 and passing through point (2,6) can be written in point-slope form as
y-6=-3%28x-2%29

The more traditional (and unique) slope-intercept form of the equation can be derived from the point-slope form above.
y-6=-3%28x-2%29 --> y-6=-3x-3%2A%28-2%29 --> y-6=-3x%2B6 --> highlight%28y=-3x%2B12%29