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

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) (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

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

The equation of a line with slope and passing through point (2,6) can be written in point-slope form as

The more traditional (and unique) slope-intercept form of the equation can be derived from the point-slope form above.
--> --> -->
RELATED QUESTIONS
The coordinates of three vertices of a parallelogram are (−3, 3), (2, 3), and (4,... (answered by MathLover1)

Three of the vertices of a parallelogram are (2, 1) (4, 7), and (6, 5). What are the... (answered by KMST)

What is the area of a parallelogram if the coordinates of its vertices are (-4, -1), (-2, (answered by mananth)

Find all the possible coordinates for the fourth vertex of a parallelogram with the given (answered by jim_thompson5910)

A parallelogram has vertices (5,0), (3,-3), (-4,-3) and (-2,0). The diagonals of the... (answered by ikleyn)

Show that the points (-1, -3) (-2, 0) (1, 6) and (2, 3) are the vertices of a... (answered by Boreal)

Points R(1, 3), S(�2, �1), and T(5, �1) are vertices of a parallelogram. Give the... (answered by KMST)

Suppose that Parallelogram ABCD has vertices A(2, 4), B(8, 4), C(5, -3) and D(-1, -3).... (answered by KMST)

In the diagram, three vertices of parallelogram ORST are O(0, 0), R(b, d), and T(a,0).... (answered by Edwin McCravy)