SOLUTION: Using slopes, find the fourth vertex of a parallelogram if (7,-1),(-3,1) and (-5,5) are it's three consecutive vertices.

Algebra ->  Parallelograms -> SOLUTION: Using slopes, find the fourth vertex of a parallelogram if (7,-1),(-3,1) and (-5,5) are it's three consecutive vertices.      Log On


   

Question 1065647: Using slopes, find the fourth vertex of a parallelogram if (7,-1),(-3,1) and (-5,5) are it's three consecutive vertices.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
.
Find the slope of the line from (-3,1) to (-5,5).
Change in y is 4, change in x is -2.
So starting at (7,-1),
(7,-1)+(-2,4)=(5,3)
.
.
.
.
.
.
.
Algebraically,
m%5B1%5D=%285-1%29%2F%28-5-%28-3%29%29=4%2F%28-2%29=-2
So then starting from (7,-1)
y-%28-1%29=-2%28x-7%29
y%2B1=-2x%2B14
y%5B1%5D=-2x%2B13
Next find the slope from (7,-1) to (-3,1),
m%5B2%5D=%281-%28-1%29%29%2F%28-3-7%29=2%2F-10=-1%2F5
Starting from (-5,5),
y-5=-%281%2F5%29%28x%2B5%29
y-5=-x%2F5-1
y%5B2%5D=-x%2F5%2B4
So now find the intersection of the two lines,
-2x%2B13=-x%2F5%2B4
-10x%2B65=-x%2B20
-9x=-45
x=5
and
y=-2%285%29%2B13
y=3
(5,3) as we already showed.
.
.
.
.