## anonymous one year ago 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? (Remember, opposite sides of a parallelogram are parallel. help !!

1. anonymous

I'm guessing x=1... I'm not sure how to solve this problem.

2. anonymous

me either ..

3. anonymous

A

4. anonymous

B

5. anonymous

C

6. anonymous

D

7. anonymous

Imagine the arrangement is as follows: |dw:1434980951791:dw|

8. anonymous

mmkay ...

9. anonymous

|dw:1434981266777:dw| The circled line is the one required, which connects two vertices. Given that they have the same gradient, then the gradient of the circled one is $\frac{ 4-1 }{ -3-(-2) }=\frac{ 3 }{ -1 }=-3$ This will also be the gradient of the new line that we are looking for. The next, moving onto the required line, to make its equation it is important to choose a point, and it will be the vertex (2,6). Using the original equation, we get $y-y _{1}=m(x-x _{1})$ Using substitution of the values... $y-6=-3(x-2)$ $y=-3x+6+6=-3x+12$

10. anonymous

y=3x-12 ? what do i do with that ?

11. anonymous

That is the answer - the required equation of the line.

12. anonymous

ooookay. thank you